CN109885865A - A kind of layered medium equivalent electrical parameter calculation method based on iteration Debye model - Google Patents
A kind of layered medium equivalent electrical parameter calculation method based on iteration Debye model Download PDFInfo
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Abstract
The invention discloses a kind of calculation method of layered medium equivalent electrical parameter based on iteration Debye model, which provides a kind of Fast numerical method for solving for the equivalent electrical parameter solution of horizontal layer structural material.Realize step are as follows: establish the equivalent circuit of two layer structure materials；It is corresponding with Debye model equivalent circuit, the electrical parameter of each layer in Debye model parameter and stratified material is established, the relationship between geometric parameter (thickness, area) calculates the equivalent electrical parameter of double layer material；It is equivalent to material known to one layer of electrical parameter by first two layers using the electrical parameter calculated, third layer is equivalent to the second layer, is constituted new bilayer model with this to calculate the equivalent electrical parameter of three-layer structure material；The equivalent electrical parameter of i-1 (i < N) layer material is as first layer before iterating to calculate, i-th layer constitutes new bilayer model as the second layer and calculates equivalent electrical parameter, increase i, until i=N layer material all calculates the equivalent electrical parameter for completing to can be obtained N layer material.
Description
Technical field
The present invention relates to mixture electrical parameter computing technique field more particularly to a kind of utilization iteration Debye (debye) moulds
The method of type calculating layered medium equivalent electrical parameter.
Background technique
Horizontal layer structural material is in the substrate of integrated circuit, and very common in microwave device, equivalent electrical parameter is
The parameter needed when design.In exploration geophysics research rammell can also Approximate Equivalent be horizontal layer structure, equivalent electricity
The solution of parameter (dielectric constant and conductivity) is extremely important.
In the prior art, the equivalent electrical parameter of layer structure material, which calculates, uses equivalent capacity model, but is built upon low
Under the premise of frequency even direct current, electrical spectrum of the equivalent electrical parameter of horizontal layer structure within the scope of broad frequency band can only then pass through
The method of Numerical Simulation obtains.Numerical Simulation method then needs to model model, subdivision, by establishing equation
Group and then solution obtain electrical parameter, and the accuracy of calculated result depends on the fine degree of mesh generation, and large-scale equation group is asked
Solution is carried out often through the mode of iteration or extensive matrix inversion, and it is longer to calculate the time.
Summary of the invention
It is an object of the invention in the equivalent electrical parameter Solve problems and its wide frequency range of horizontal multilayer material
Dispersion phenomenon, a kind of calculation method of layered medium equivalent electrical parameter based on iteration Debye model is provided.
In order to realize above-mentioned task, the invention adopts the following technical scheme:
A kind of calculation method of the layered medium equivalent electrical parameter based on iteration Debye model, comprising the following steps:
For the layered medium of the horizontal layer structure with N layer material, pair of first layer, the second layer material is initially set up
Layer model equivalent circuit, the equivalent circuit of bilayer model is corresponding with Debye model equivalent circuit, establish Debye model parameter with
Relationship in layered medium between the electrical parameter of each layer, geometric parameter calculates the equivalent electrical parameter of first layer, the second layer material；
Using calculated equivalent electrical parameter, first layer, the second layer material are equivalent to material known to one layer of electrical parameter,
The third layer material of layered medium is equivalent to the second layer material, new bilayer model is constituted with this to calculate first layer to third
The equivalent electrical parameter of layer material；
The equivalent electrical parameter of i-1 layer material is equivalent to the first layer material, the equivalent second layer material of the i-th layer material before iterating to calculate
Material is constituted new bilayer model with this and calculates equivalent electrical parameter, completes to can be obtained N layer material until i=N material all calculates
Horizontal layer structure layered medium equivalent electrical parameter.
Further, the bilayer model equivalent circuit of the first layer, the second layer material, specific establishment process are as follows:
Remember the relative dielectric constant of first layer, the second layer material, conductivity, thickness and horizontal direction surface area are respectively as follows:
εrk,σk,dk,Ak(k=1,2), wherein Y1For the equivalent admittance of the first layer material, Y2For the equivalent admittance of the second layer material, then:
Y1=G1+jωC1；Y2=G2+jωC2
The then equivalent resultant admittance of bilayer model are as follows:
Wherein, C1, C2, G1, G2Relationship between material parameter are as follows:
In above formula, ε0For the dielectric constant in vacuum, by YtotalIt is extended to the plural form of real and imaginary parts composition:
Further, the equivalent circuit by bilayer model is corresponding with Debye model equivalent circuit, comprising:
The resultant admittance of the equivalent circuit of Debye model are as follows:
Wherein ω is angular frequency, and τ is relaxation factor, C∞Indicate capacitor of the model in high-frequency, CsIndicate model low
Capacitor when frequency, GsIndicate conductance of the model in low frequency；
By the real part of the equivalent resultant admittance of the bilayer model and Debye model resultant admittance, imaginary part is equal to each other respectively, can
:
By the component values in the available Debye model equivalent circuit of above-mentioned two formula:
Further, described to establish in Debye model parameter and layered medium between the electrical parameter of each layer, geometric parameter
Relationship calculates the equivalent electrical parameter of first layer, the second layer material, comprising:
The calculation formula of Debye model effective dielectric constant and equivalent conductivity is respectively as follows:
Wherein εsDielectric constant when for low frequency, σsConductivity when for low frequency, ε∞For the dielectric constant of high frequency treatment, ω is
Angular frequency, τ are relaxation factor；
The relationship between parameter and material parameter in Debye model is as follows:
Four parameters are substituted into εeffAnd σeffExpression formula, the equivalent electrical parameter of bilayer model can be obtained, i.e., equivalent dielectric
Constant εreff(12)(ω) and equivalent conductivity σeff(12)(ω)。
Further, described using calculated equivalent electrical parameter, first layer, the second layer material are equivalent to one layer of electricity
The third layer material of layered medium is equivalent to the second layer material by material known to parameter, is constituted new bilayer model with this
Calculate the equivalent electrical parameter of first layer to third layer material, comprising:
The relative dielectric constant of first layer to third layer material is respectively as follows: εr1,εr2,εr3, conductivity is respectively as follows: σ1,σ2,
σ3, thickness is respectively d1,d2,d3, horizontal direction surface area is respectively A1,A2,A3；
First layer to third layer material design parameter are as follows:
Y3=G3+jωC3
Wherein A1=A2, and:
For the equivalent circuit component values for the new material that first layer and the second layer are constituted, and
For the equivalent circuit component values of third layer material；Then:
Wherein εreff(12)s, σeff(12)sDielectric constant and conductivity of the bilayer model in low frequency respectively,
εreff(12)∞, σeff(12)∞Dielectric constant and conductivity of the bilayer model in high frequency respectively, dtotal=d1+d2+d3；It will
These parameters substitute into effective dielectric constant and equivalent conductivity formula can be obtained Three-tier Architecture Model in entire frequency band etc.
Imitate electrical parameter.
The present invention has following technical effect that compared with prior art
Iteration Debye model proposed by the present invention, the electrical parameter of rapid solving sandwich by way of iteration
Change curve in broad frequency range.This method is established on the basis of the equivalent circuit of model, and model ginseng has been accurately accounted for
Influence of the number (thickness, the conductivity of layers of material, dielectric constant) to lump component values in circuit structure, for further analysis
Influence of the model parameter to electrical parameter provides a kind of approach.This method is simple, and efficiently, precision is high, calculates the time much smaller than biography
The method of system provides a kind of effective electrical parameter in electricity, materialogy and applied physics field for horizontal layer material and asks
Solution method.
Detailed description of the invention
Fig. 1 is N layers of horizontal layer material model schematic diagram；
Fig. 2 is two layers of horizontal layer material model schematic diagram；
Fig. 3 is the equivalent circuit diagram of two-layer model；
Fig. 4 is the equivalent circuit diagram of Debye model；
Fig. 5 is three levels stratified material model schematic；
Fig. 6 is the equivalent circuit diagram of three layer model；
Fig. 7 is the equivalent electrical parameter of three layer model and the comparison diagram of finite difference method calculated result；
Fig. 8 is the iteration Debye model schematic diagram that multiple-layer horizontal stratified material model equivalent electrical parameter calculates.
Specific embodiment
(effective dielectric constant and equivalent conductivity are with frequency for wideband charging property spectrum of the present invention to horizontal layer structural material
Change curve) Solve problems, the equivalent circuit of bilayer model is initially set up, according to its equivalent electricity of Debye model parametric solution
Parametric solution is iterated.
As shown in Figures 1 to 8, for solve broad frequency range in N (N > 3) layer horizontal layer structure layered medium it is equivalent
Electrical parameter, the invention discloses a kind of calculation methods that the layered medium multilayer material based on iteration Debye model is electrically composed.It should
The detailed step of method is as follows:
Step 1, the equivalent circuit of bilayer model is established
Fig. 1 is the N layer material model to be solved, and Fig. 2, which is shown, takes layers 1 and 2 in N layer material, one of foundation
Horizontal duplex material model.The relative dielectric constant of materials at two layers, conductivity, thickness and horizontal direction surface area are respectively as follows: εrk,
σk,dk,Ak(k=1,2), equivalent-circuit model is as shown in figure 3, wherein Y1For the equivalent admittance of the first layer material, Y2It is second
The equivalent admittance of layer material:
Y1=G1+jωC1；Y2=G2+jωC2
The then equivalent resultant admittance of bilayer model are as follows:
Wherein, C1, C2, G1, G2Relationship between material parameter are as follows:
In above formula, ε0For the dielectric constant in vacuum, by YtotalIt is extended to the plural form of real and imaginary parts composition:
Step 2, the equivalent circuit of bilayer model is corresponding with the equivalent circuit of Debye model
The equivalent circuit of Debye model is as shown in figure 4, its resultant admittance are as follows:
Wherein ω is angular frequency, and τ is relaxation factor, C∞Indicate capacitor of the model in very high frequency, CsIndicate that model exists
Capacitor when low frequency, GsIndicate conductance of the model in low frequency.The equivalent of double_layer construction model that step 1 obtains always is led
The real part received with Debye model resultant admittance, imaginary part are equal to each other respectively, can be obtained:
By the component values in the available Debye model equivalent circuit of above-mentioned two formula:
Step 3, the relationship in Debye model parameter and layered medium between the electrical parameter of each layer, geometric parameter is established, is counted
Calculate the equivalent electrical parameter of first layer, the second layer material
Debye model is a kind of generally acknowledged method that can be calculated material and answer dielectric spectra, effective dielectric constant and equivalent
The calculation formula of conductivity is respectively as follows:
Wherein εsDielectric constant when for low frequency, σsConductivity when for low frequency, ε∞For the dielectric constant of high frequency treatment, ω is
Angular frequency, τ are relaxation factor, and the component values in the Debye model equivalent circuit as obtained in step 2 can obtain, Debye model
In parameter and material parameter between relationship it is as follows:
Four parameters are substituted into εeffAnd σeffExpression formula, the equivalent electricity of bilayer model (first layer, the second layer) can be obtained
Parameter, i.e. effective dielectric constant and equivalent conductivity.
Step 4, the calculating of trilaminate material equivalent electrical parameter
Using calculated equivalent electrical parameter, first layer, the second layer material are equivalent to material known to one layer of electrical parameter,
The third layer material of layered medium is equivalent to the second layer material, new bilayer model is constituted with this to calculate first layer to third
The equivalent electrical parameter of layer material, the specific steps are as follows:
If the bilayer model equivalent electrical parameter being calculated by step 1-3 are as follows: effective dielectric constant εreff(12)(ω), it is equivalent
Conductivityσeff(12)(ω), they are the functions of frequency, and when low frequency, that is, ω goes to zero or high frequency is when i.e. ω tends to ∞,
εreff(12)(ω)、σeff(12)The value of (ω) is constant；Dielectric constant, conductivity when low frequency are denoted as ε respectivelyreff(12)s,
σeff(12)s, dielectric constant, conductivity when by high frequency are denoted as ε respectivelyreff(12)∞, σeff(12)∞。
First layer, the second layer material are equivalent to a thickness of d1+d2, relative dielectric constant εreff(12)(ω), conductivity
For σeff(12)One layer of medium of (ω).
The structure of trilaminate material model is as shown in figure 5, the relative dielectric constant of layers of material is respectively as follows: εr1,εr2,εr3,
Conductivity is respectively as follows: σ1,σ2,σ3, thickness is respectively d1,d2,d3, horizontal direction surface area is respectively A1,A2,A3, first layer and
Two layers are equivalent to one layer of electrical parameter medium varying with frequency, it and third layer medium constitute a new double-layer structure.It is similar
Ground can obtain its equivalent circuit as shown in fig. 6, design parameter according to step 1 are as follows:
Y12=G12(ω)+jωC12(ω)
Y3=G3+jωC3
Wherein Y12For the equivalent admittance of first layer, the second layer material, Y3For the equivalent admittance of third layer material, YtotalIt is
One layer of equivalent resultant admittance to third layer material, A1=A2, and:
For the equivalent circuit component values of " new " material that first layer and the second layer are constituted, and
For the equivalent circuit component values of third layer material；Then:
Wherein τ (ω) is relaxation factor, is the function of frequency；εreff(12)s, σeff(12)sRespectively step 3 is calculated
Dielectric constant and conductivity of the bilayer model in low frequency, εreff(12)∞, σeff(12)∞The respectively double-mold that is calculated of step 3
Dielectric constant and conductivity of the type in high frequency, dtotal=d1+d2+d3；These parameters are substituted into effective dielectric constant and equivalent electricity
Conductance formula can be obtained equivalent electrical parameter of the Three-tier Architecture Model in entire frequency band.It is illustrated in figure 7 and is mentioned using the present invention
Three-decker equivalent electrical parameter calculated result that iteration Debye model out is calculated and finite difference method calculated result
Comparative situation, as seen from the figure, the two are coincide good, it was demonstrated that the correctness of present invention proposition method.
Step 5, the equivalent electrical parameter of i-1 layer material is equivalent to the first layer material before iterating to calculate, the i-th layer material equivalent the
Two layer materials are constituted new bilayer model with this and calculate equivalent electrical parameter, complete to can be obtained N until i=N material all calculates
The equivalent electrical parameter of the layered medium of the horizontal layer structure of layer material.
If N=4, step 4 has obtained the electrical parameter of Three-tier Architecture Model, and three first layers structure is equivalent to " first layer ",
Four-layer structure is equivalent to " second layer ", is constituted a new bilayer model with this." first layer " of this new equivalent model
For mixture, electrical parameter changes with frequency, and " second layer " is dielectric constant and conductivity is the pure substance of constant.It is equivalent
The equivalent electrical parameter of " bilayer model " afterwards can be according to the equivalent electrical parameter of the Debye model parameter formula in step 4 and step 3
Calculation formula and obtain.Similarly, 5 layers, 6 layers ... isostructural equivalent electrical parameters can calculate acquisition by way of iteration.
It is illustrated in figure 8 the flow chart that iteration Debye model calculates layer structure equivalent electrical parameter.
Claims (5)
1. a kind of calculation method of the layered medium equivalent electrical parameter based on iteration Debye model, which is characterized in that including following
Step:
For the layered medium of the horizontal layer structure with N layer material, the double-mold of first layer, the second layer material is initially set up
Type equivalent circuit, the equivalent circuit of bilayer model is corresponding with Debye model equivalent circuit, establish Debye model parameter and layering
Relationship in medium between the electrical parameter of each layer, geometric parameter calculates the equivalent electrical parameter of first layer, the second layer material；
Using calculated equivalent electrical parameter, first layer, the second layer material are equivalent to material known to one layer of electrical parameter, will be divided
The third layer material of layer medium is equivalent to the second layer material, is constituted new bilayer model with this to calculate first layer to third layer material
The equivalent electrical parameter of material；
The equivalent electrical parameter of i-1 layer material is equivalent to the first layer material before iterating to calculate, equivalent second layer material of the i-th layer material,
New bilayer model is constituted with this and calculates equivalent electrical parameter, completes to can be obtained N layer material until i=N material all calculates
The equivalent electrical parameter of the layered medium of horizontal layer structure.
2. the calculation method of the layered medium equivalent electrical parameter based on iteration Debye model as described in claim 1, feature
It is, the bilayer model equivalent circuit of the first layer, the second layer material, specific establishment process are as follows:
Remember the relative dielectric constant of first layer, the second layer material, conductivity, thickness and horizontal direction surface area are respectively as follows: εrk,
σk,dk,Ak(k=1,2), wherein Y1For the equivalent admittance of the first layer material, Y2For the equivalent admittance of the second layer material, then:
Y1=G1+jωC1；Y2=G2+jωC2
The then equivalent resultant admittance of bilayer model are as follows:
Wherein, C1, C2, G1, G2Relationship between material parameter are as follows:
In above formula, ε0For the dielectric constant in vacuum, by YtotalIt is extended to the plural form of real and imaginary parts composition:
3. the calculation method of the layered medium equivalent electrical parameter based on iteration Debye model as described in claim 1, feature
It is, the equivalent circuit by bilayer model is corresponding with Debye model equivalent circuit, comprising:
The resultant admittance of the equivalent circuit of Debye model are as follows:
Wherein ω is angular frequency, and τ is relaxation factor, C∞Indicate capacitor of the model in high-frequency, CsIndicate model in low frequency
Capacitor, GsIndicate conductance of the model in low frequency；
By the real part of the equivalent resultant admittance of the bilayer model and Debye model resultant admittance, imaginary part is equal to each other respectively, can be obtained:
By the component values in the available Debye model equivalent circuit of above-mentioned two formula:
4. the calculation method of the layered medium equivalent electrical parameter based on iteration Debye model as described in claim 1, feature
It is, the relationship established in Debye model parameter and layered medium between the electrical parameter of each layer, geometric parameter, calculates first
The equivalent electrical parameter of layer, the second layer material, comprising:
The calculation formula of Debye model effective dielectric constant and equivalent conductivity is respectively as follows:
Wherein εsDielectric constant when for low frequency, σsConductivity when for low frequency, ε∞For the dielectric constant of high frequency treatment, ω is angular frequency
Rate, τ are relaxation factor；
The relationship between parameter and material parameter in Debye model is as follows:
Four parameters are substituted into εeffAnd σeffExpression formula, the equivalent electrical parameter of bilayer model, i.e. effective dielectric constant can be obtained
εreff(12)(ω) and equivalent conductivity σeff(12)(ω)。
5. the calculation method of the layered medium equivalent electrical parameter based on iteration Debye model as described in claim 1, feature
It is, it is described using calculated equivalent electrical parameter, first layer, the second layer material are equivalent to material known to one layer of electrical parameter
Material, is equivalent to the second layer material for the third layer material of layered medium, is constituted new bilayer model with this to calculate first layer extremely
The equivalent electrical parameter of third layer material, comprising:
The relative dielectric constant of first layer to third layer material is respectively as follows: εr1,εr2,εr3, conductivity is respectively as follows: σ1,σ2,σ3, thick
Degree is respectively d1,d2,d3, horizontal direction surface area is respectively A1,A2,A3；
First layer to third layer material design parameter are as follows:
Y3=G3+jωC3
Wherein A1=A2, and:
For the equivalent circuit component values for the new material that first layer and the second layer are constituted, and
For the equivalent circuit component values of third layer material；Then:
Wherein εreff(12)s, σeff(12)sDielectric constant and conductivity of the bilayer model in low frequency respectively, εreff(12)∞,
σeff(12)∞Dielectric constant and conductivity of the bilayer model in high frequency respectively, dtotal=d1+d2+d3；By these parameters
It substitutes into effective dielectric constant and equivalent conductivity formula can be obtained equivalent electrical parameter of the Three-tier Architecture Model in entire frequency band.
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