CN111814358A - Multi-factor co-optimization design method for comprehensive performance of microwave composite dielectric substrate - Google Patents
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- 239000000758 substrate Substances 0.000 title claims abstract description 36
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- 239000002131 composite material Substances 0.000 title claims abstract description 31
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- 230000000694 effects Effects 0.000 claims abstract description 15
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- 239000000463 material Substances 0.000 claims abstract description 13
- 239000002994 raw material Substances 0.000 claims abstract description 13
- 238000002474 experimental method Methods 0.000 claims abstract description 8
- 230000001419 dependent effect Effects 0.000 claims description 18
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- VYPSYNLAJGMNEJ-UHFFFAOYSA-N silicon dioxide Inorganic materials O=[Si]=O VYPSYNLAJGMNEJ-UHFFFAOYSA-N 0.000 description 23
- 239000000919 ceramic Substances 0.000 description 21
- 239000000843 powder Substances 0.000 description 21
- 229910052681 coesite Inorganic materials 0.000 description 20
- 229910052906 cristobalite Inorganic materials 0.000 description 20
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- 229910052682 stishovite Inorganic materials 0.000 description 20
- 229910052905 tridymite Inorganic materials 0.000 description 20
- 239000002245 particle Substances 0.000 description 12
- 229920001343 polytetrafluoroethylene Polymers 0.000 description 11
- 239000004810 polytetrafluoroethylene Substances 0.000 description 11
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- RYGMFSIKBFXOCR-UHFFFAOYSA-N Copper Chemical compound [Cu] RYGMFSIKBFXOCR-UHFFFAOYSA-N 0.000 description 1
- -1 Polytetrafluoroethylene Polymers 0.000 description 1
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Abstract
The invention discloses a multi-factor co-optimization design method for comprehensive performance of a microwave composite dielectric substrate. The method combines variance analysis, a general linear model, factor effect analysis, an overlapping contour line method and a response optimizer, and solves the problem of multi-factor co-optimization of the comprehensive performance of the substrate. The optimum specification and the optimum formula parameters of the raw materials can be obtained, and the multi-factor joint optimization of comprehensive performance is met. The problems of huge experiment amount, expensive experiment cost and the like in multi-factor co-optimization design of the comprehensive performance of the substrate are solved, and the problem of mutual restriction relation among the comprehensive performance of the substrate is effectively solved. The prepared material is used in the field of microwave signal transmission, effectively improves the signal transmission speed, ensures the fidelity of high-frequency signals, reduces the energy transmission loss, has a near-zero temperature coefficient, is favorable for the use of substrate products in different temperature occasions, simultaneously meets the substrate material with multiple properties and co-optimization, and can meet the harsh application conditions of high-frequency and high-speed circuit boards.
Description
Technical Field
The invention relates to a design method of comprehensive performance of a microwave composite dielectric substrate in the field of high-frequency communication, in particular to a multi-factor co-optimization design method of the comprehensive performance of the microwave composite dielectric substrate.
Background
The rapid development of radio communication technology has made urgent demands on miniaturization, light weight and high integration of electronic products. The microwave communication technology is gradually and widely applied by virtue of the advantages of strong wide bandwidth, high frequency, low loss and the like in millimeter wave bands. In order to realize these functions, designers of printed circuit boards must continuously increase the wiring density and the number of layers of lines, which presents unprecedented challenges to the substrate for high-frequency signal transmission. Microwave communication circuits require that the substrate must first have a constant relative dielectric constant, very low energy loss, thermal expansion properties close to those of copper foil, very low water absorption, good dimensional stability and very precise thickness tolerances, while the board must also have good processability. In fact, however, the substrate itself is a composite material consisting of inorganic fillers, organic polymers, reinforcing materials and additives, the properties of the material itself determining the mutual constraints between certain targets of the board, and even the trade-off. Therefore, in the formulation design and the process design, the comprehensive influence of various factors such as the type, specification and components of the raw materials on the final performance must be comprehensively measured, and the joint optimization of the comprehensive performance can be met.
In order to meet the stringent requirements of multiple properties of a substrate product, the specification and the amount of raw materials need to be screened and optimized according to a target, and in the process, if a traditional experimental method is adopted, two problems are easy to occur: firstly, the same raw material often has different specifications, and it is difficult to judge which specification is most suitable for multi-target co-optimization of the composite material in advance; secondly, the ratio of different components of the same raw material often has a decisive influence on the material performance, but the traditional experimental design generally only modulates one factor and fixes other factors, so that the obtained experimental result is limited, and the optimal formula ratio is easy to miss. Therefore, a scientific and reasonable technical means and method are urgently needed to develop formula design, reasonable screening, simulation, analysis and prediction are carried out through professional analysis software, and then the relationship between the multi-target result and the multi-influence factors influencing the composite material is established, so that a theoretical basis is provided for rapidly determining the optimal formula of the composite material.
Disclosure of Invention
In view of the problems of the existing microwave composite medium substrate comprehensive performance design technology, the invention aims to provide a multi-factor co-optimization design method for the comprehensive performance of a microwave composite medium substrate.
The technical scheme adopted by the invention is as follows: a multi-factor co-optimization design method for comprehensive performance of a microwave composite dielectric substrate is characterized by comprising the following steps:
the method comprises the following steps: the performance target of the product to be researched is determined, particularly, a plurality of performance targets and requirements which must realize co-optimization are taken as key indexes, and a material table is matched according to the performance targets;
step two: determining different specifications of raw materials of each component in the material table and upper and lower limit values of the component of the raw materials of each component, and making an experimental scheme plan table.
Step three: carrying out experiments according to the experimental scheme schedule, collecting data, and respectively obtaining data according to statistics → anova → general linear model in minitab softwareFitting equations of each key target; the key index dependent variables are a plurality of, the assumed number is m, and each key target dependent variable is Y1,Y2......Ym(ii) a Meanwhile, there are several factors affecting the key index, and assuming that the number is n, each factor affecting the key index is X1,X2......Xn(ii) a Through a general linear model in minitab software, a fitting equation of each key target dependent variable including each factor is obtained as follows:
Yi=ai+ΣbijXj,i=1,2，...m；j=1,2,...n；------（1）
in formula (1): a isiIs a constant of each dependent variable in the fitting equation;
bijare the coefficients of the factors in the fitting equation.
Step four: obtaining a fitting line graph of the factor effect according to the influence effect of each factor on the product performance target in the fitting equation, wherein the larger the slope of the fitting line graph is, the more remarkable the influence is, the slope represents the change trend, when the slopes of the fitting line graphs of the two factor effects have positive and negative directions, the change trends of the two factors are opposite, and the factors have a mutual restriction relationship.
Step five: and (3) respectively confirming the co-optimization areas of the key targets with the mutual constraint relation by using an overlapped contour line method tool of minitab software, wherein the solid line and the dotted line of each line in the overlapped contour diagram respectively represent the lower limit value and the upper limit value of each factor, and the blank area where the solid line and the dotted line are intersected is the combined area where each key dependent variable achieves co-optimization.
Step six: a response optimizer using minitab software observes the trend of changes over the entire range of key dependent variables, and the response optimizer explicitly identifies a set of responsive input factor setting combinations and predicted output results.
The invention has the following beneficial effects: the method combines variance analysis, a general linear model, factor effect analysis, an overlapping contour line method and a response optimizer, realizes a multi-factor co-optimization design method of the comprehensive performance of the microwave composite medium substrate, and solves the problem of multi-factor co-optimization of the comprehensive performance of the microwave composite medium substrate. The optimal specification and optimal formula parameters of the raw materials can be obtained by using a scientific analysis method, and the prepared substrate material can simultaneously meet the multi-factor joint optimization of comprehensive performance. The optimal combination of the specification and the content of each component in the material table can be determined to obtain the optimal formula, and the microwave composite medium substrate product prepared by using the formula can realize multi-factor co-optimization of comprehensive performance. The method solves the practical problems of huge experimental amount, expensive experimental cost and the like in the multi-factor co-optimization design of the comprehensive performance of the microwave composite dielectric substrate, and can effectively solve the problem of mutual restriction relationship in the comprehensive performance of the substrate and even the co-optimization under the condition that multiple performances are mutually contradictory.
The material with low dielectric constant prepared by the method is used in the field of microwave signal transmission, can effectively improve the signal transmission speed, ensure the fidelity of high-frequency signals, reduce the loss of energy transmission, and ensure the near-zero temperature coefficient, is favorable for the use of substrate products in different temperature occasions, and simultaneously meets the requirements of multi-performance co-optimized substrate materials and the harsh application conditions of high-frequency high-speed circuit boards.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2 is a diagram illustrating the main effects of a critical target relative permittivity model according to an embodiment of the present invention;
FIG. 3 is a diagram of the main effects of a critical target temperature coefficient of permittivity model in accordance with an embodiment of the present invention;
FIG. 4 is an overlapping contour plot of a key object of an embodiment of the present invention;
FIG. 5 is a diagram of the response optimizer results for the key objectives of the embodiment of the present invention.
Detailed Description
The invention is further illustrated by the following examples in conjunction with the accompanying drawings:
referring to FIG. 1, PTFE/SiO with low dielectric constant and low temperature coefficient2For example, the microwave composite dielectric substrate is a multi-factor co-optimization design method for comprehensive performance of the microwave composite dielectric substrate, which includes the following stepsThe method comprises the following steps:
the method comprises the following steps: it is clear that a product to be researched belongs to the field of high-frequency application, the temperature stability of the dielectric constant of the microwave composite dielectric substrate in the field is one of the most important properties of the substrate, and the closer the temperature coefficient is to zero, the better the temperature coefficient is, the more the dielectric property of the substrate is slightly changed by the fluctuation of the temperature. The designed target value of the dielectric constant of the product is 2.94, and the designed target value of the temperature coefficient is 0 ppm/DEG C. PTFE (Polytetrafluoroethylene) and SiO according to the nature of the substance2Ceramic powder (hereinafter abbreviated as SiO)2) Theoretical dielectric constants of 2.1 and 4.0, theoretical values of-400 and 27.8 ppm/deg.C, PTFE and SiO can be selected2Is the main raw material, but different grain sizes and different contents of SiO2Both cause variations in dielectric constant and temperature coefficient. Therefore, two factors of the grain diameter and the content of the ceramic powder need to be regulated and controlled to achieve the co-optimization of two properties of the dielectric constant and the temperature coefficient.
Step two: determining the specification of raw materials of each component in a material table, the limiting values of the upper and lower boundaries of each component element, and SiO2The average particle diameter D50 was 8, 18 and 26 μm, respectively, SiO2The contents are respectively 0.58, 0.60, 0.62 and 0.64. The numbers of the samples are sequentially formed into an experimental scheme schedule, and the specific content is shown in table 1. Wherein, the sample number simultaneously represents the grain diameter and the content of the ceramic powder, the former figures represent the grain diameter, and A, B, C, D respectively represent different contents (0.58-0.64). Namely: 8-A represents SiO2Particle size of 8 μm, SiO2The content is 0.58; 8-B represents SiO2Particle size of 8 μm, SiO2The content is 0.60; by analogy, 26-D represents SiO2Particle size of 26 μm, SiO2The content was 0.64.
TABLE 1 results of dielectric constant and temperature coefficient for different samples
Step three: the experiments were performed according to the protocol schedule and data were collected with the results shown in table 1. According to fitting equation Yi=ai+ΣbijXjI =1,2,. m; j =1,2,. n; obtaining fitting equations of dielectric constant and temperature coefficient key targets respectively in formula (1), and obtaining fitting equations of dielectric constant and temperature coefficient key targets respectively when m =2 and n =2 in formula (1):
Y1=a1+b11X1+b12X2---------------（2）
Y2=a2+b21X1+b22X2---------------（3）
fitting equation (2), Y, with the factors and dependent variables of the examples1Stands for PTFE/SiO2Dielectric constant at room temperature of composite material, use ofrRepresents; x1Represents SiO2The grain diameter of the ceramic powder is represented by A; x2Represents SiO2The content of the ceramic powder is represented by B; a is1Stands for PTFE/SiO2A constant of the dielectric constant of the composite material; b11The dependent variable is Y1X in the fitting equation of (1)1The coefficient of (a); b12The dependent variable is Y1X in the fitting equation of (1)2The coefficient of (a); .
In the fitting equation (3), Y2Stands for PTFE/SiO2Temperature coefficient of composite material, inRepresents; x1Represents SiO2The grain diameter of the ceramic powder is represented by A; x2Represents SiO2The content of the ceramic powder is represented by B; a is2Stands for PTFE/SiO2A constant of the temperature coefficient of the composite material; b21The dependent variable is Y2X in the fitting equation of (1)1The coefficient of (a); b22The dependent variable is Y2X in the fitting equation of (1)2The coefficient of (a); through a minitab software general linear model, the method can obtain a linear model containing A, B two factorsrAnd τFitting equation of two key target dependent variables.
When Y is1=r；X1=A；X2=B；a1=1.9193；b11=0.002857；b12=1.582；Y2=τ；a2=-468.9；b21=0.224；b22When =758, the following two fitting equations are obtained from the fitting equations (2) and (3), respectively:
r=1.9193+0.002857A+1.582B------（4）
τ=-468.9+0.224A+758B-----------（5）
and each item coefficient in the fitting equation is calculated by a least square method.
Step four: according to the fitting equation, the influence effect of each factor on the product target is obtained, as shown in fig. 2 and 3, and as seen from fig. 2 and 3, a constraint relationship exists between the relative dielectric constant and the temperature coefficient. As can be seen from fig. 2, the dielectric constant is affected by the particle size and the content of the ceramic powder, and the effect of the content of the ceramic powder is more significant than the effect of the particle size of the ceramic powder. As can be seen from fig. 3, the ceramic powder content factor has a more significant effect than the particle size factor in terms of temperature coefficient. This indicates that the variation in the content of the ceramic powder contributes more to the variation in the temperature coefficient. Simultaneous control of the levels of both factors is required to achieve co-optimization of the goals.
Step five: the key targets with the mutual constraint relation are respectively subjected to co-optimization area confirmation by using an overlapping contour line method tool of minitab software, fig. 4 is an overlapping contour line graph of relative dielectric constant and temperature coefficient, wherein a gray solid line and a gray dotted line respectively represent lower limit and upper limit values (2.93 and 2.95) of the relative dielectric constant, a black solid line and a black dotted line respectively represent lower limit and upper limit values (-4 and 4 ppm/DEG C) of the temperature coefficient, and the parts between the solid line and the dotted line of two colors are respectively ceramic powder particle size and content parameter combinations falling between the upper limit and the lower limit. The white areas where they intersect, then, are the combined areas where co-optimization is achieved for both models, suggesting that it is theoretically possible to achieve co-optimization of both relative permittivity and temperature coefficient.
Step six: the response optimizer is a scientific tool in minitab software for determining the optimal setting of the predicted variables, and can explicitly identify a set of input factor setting combinations for response and predicted output results. In this embodiment, the response variable optimizer is used to predict the result of any combination of parameters with the ceramic powder particle size ranging from 8 μm to 26 μm and the ceramic powder content ranging from 0.58 μm to 0.64 m, and the predicted result is shown in fig. 5. As can be seen from fig. 5, when the particle size of the ceramic powder is 18.0 μm and the content of the ceramic powder is 0.6133, that is: when a = 18; when B =0.6133, it is derived from equations (4) and (5) in the step three fitting equation:
r=1.9193+0.002857A+1.582B=1.9193+0.002857×18+1.582×0.6133；
τ=-468.9+0.224A+758B=-468.9+0.224×18+758×0.6133；
calculated to obtain the relative dielectric constantrPredicted value is 2.941, temperature coefficient tauThe predicted value is 0.01 ppm/deg.C, these two fit values are very close to the response optimizer predicted values of FIG. 5. The performance of the substrate prepared by the formula can meet the dielectric performance requirement of high-frequency microwave circuit application on the composite material.
According to the embodiment, the method combines variance analysis, a general linear model, factor effect analysis, an overlapping contour line method and a response optimizer, and realizes a multi-factor co-optimization design method for the comprehensive performance of the microwave composite dielectric substrate. The experiment cost can be greatly reduced by limited times (12 times in the embodiment) by utilizing a scientific analysis method; by using the response optimizer analysis method, the optimal parameter composition including all significant items can be obtained that when the content of the ceramic powder is 0.6133, the particle size of the ceramic powder is 18.0 μm, the predicted value of the relative dielectric constant is 2.941, and the predicted value of the temperature coefficient is 0.01 ppm/DEG C. Experiments prove that the optimal combination obtained by the theoretical model is used, the ceramic powder with the average particle size D50=18 μm is used as a raw material to prepare the PTFE/SiO2 composite material with the ceramic powder content of 0.6133, four continuous batches of PTFE/SiO2 composite materials are tested, the mean values of the PTFE/SiO2 composite materials are 2.941 ppm/DEG C and 1.11 ppm/DEG C respectively, and the verification result is good. The microwave composite dielectric substrate prepared by the optimal parameter combination obtained by the design method meets the multi-factor co-optimization of comprehensive performance. The method solves the practical problems of huge experimental amount, expensive experimental cost and the like in the multi-factor co-optimization design of the comprehensive performance of the microwave composite dielectric substrate, and most importantly, the method can effectively solve the problem of mutual restriction relationship in the comprehensive performance of the substrate and even the co-optimization under the condition that multiple performances are mutually contradictory. When more factors and more performances are analyzed, a pairwise combination and gradual analysis method can be adopted, the steps from the second step to the fifth step in the method are repeatedly implemented, and finally, a response optimizer tool in the sixth step is adopted to accurately calculate and obtain the optimal parameter combination containing all the significant factors.
Claims (1)
1. A multi-factor co-optimization design method for comprehensive performance of a microwave composite dielectric substrate is characterized by comprising the following steps:
the method comprises the following steps: the performance target of the product to be researched is determined, particularly, a plurality of performance targets and requirements which must realize co-optimization are taken as key indexes, and a material table is matched according to the performance targets;
step two: determining different specifications of raw materials of each component in a material table and upper and lower limit values of the component of the raw materials of each component, and making an experimental scheme plan table;
step three: carrying out an experiment according to an experimental scheme schedule, collecting data, and respectively obtaining fitting equations of each key target according to statistics → anova → a general linear model in minitab software; the key index dependent variables are a plurality of, the assumed number is m, and each key target dependent variable is Y1,Y2......Ym(ii) a Meanwhile, there are several factors affecting the key index, and assuming that the number is n, each factor affecting the key index is X1,X2......Xn(ii) a Through a general linear model in minitab software, a fitting equation of each key target dependent variable including each factor is obtained as follows:
Yi=ai+ΣbijXj,i=1,2，...m；j=1,2,...n；------（1）
in formula (1): a isiIs a constant of each dependent variable in the fitting equation;
bijis the coefficient of each factor in the fitting equation;
step four: obtaining a fitting line graph of the factor effect according to the influence effect of each factor on the product performance target in the fitting equation, wherein the larger the slope of the fitting line graph is, the more remarkable the influence is, the slope represents the change trend, when the slopes of the fitting line graphs of the two factor effects have positive and negative directions, the change trends of the two factors are opposite, and the factors have a mutual restriction relationship;
step five: respectively confirming co-optimization areas of key targets with mutual constraint relation by using an overlapped contour line method tool of minitab software, wherein a solid line and a dotted line of each line in an overlapped contour diagram respectively represent the lower limit value and the upper limit value of each factor, and a blank area where the solid line and the dotted line are intersected is a combined area where each key dependent variable achieves co-optimization;
step six: a response optimizer using minitab software observes the trend of changes over the entire range of key dependent variables, and the response optimizer explicitly identifies a set of responsive input factor setting combinations and predicted output results.
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| US6187663B1 (en) * | 1999-01-19 | 2001-02-13 | Taiwan Semiconductor Manufacturing Company | Method of optimizing device performance via use of copper damascene structures, and HSQ/FSG, hybrid low dielectric constant materials |
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Application publication date: 20201023 |