CN111259534A - Equivalent electromagnetic parameter extraction method of gradient honeycomb wave-absorbing material - Google Patents

Equivalent electromagnetic parameter extraction method of gradient honeycomb wave-absorbing material Download PDF

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CN111259534A
CN111259534A CN202010031384.9A CN202010031384A CN111259534A CN 111259534 A CN111259534 A CN 111259534A CN 202010031384 A CN202010031384 A CN 202010031384A CN 111259534 A CN111259534 A CN 111259534A
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陈海燕
沈荣博
饶鸿
丰安旭
邓龙江
谢建良
陆海鹏
张丽
周志鹏
李小秋
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University of Electronic Science and Technology of China
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Abstract

The invention belongs to the technical field of computational electromagnetism, and particularly relates to an equivalent electromagnetic parameter extraction method of a gradient honeycomb wave-absorbing material. The invention solves the multivalue problem by adopting an imaginary part phase compensation method; the influence of the unique gradient structure of the gradient honeycomb wave-absorbing material on equivalent parameters is considered, namely the electromagnetic wave-absorbing material mainly comprises the coating thickness of an electromagnetic wave incident end, the coating thickness of an electromagnetic wave emergent end, the number of gradient layers of the gradient honeycomb wave-absorbing material, and physical size parameters such as increment between adjacent gradient coatings, so that the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material are extracted. The technical scheme of the invention has the advantages of simple principle and convenient use, and the obtained equivalent electromagnetic parameters are relatively accurate.

Description

Equivalent electromagnetic parameter extraction method of gradient honeycomb wave-absorbing material
Technical Field
The invention belongs to the technical field of computational electromagnetism, and particularly relates to an equivalent electromagnetic parameter extraction method of a gradient honeycomb wave-absorbing material.
Background
The honeycomb wave-absorbing material is a material which imitates a natural honeycomb hexagonal structure and has the characteristic of absorbing electromagnetic waves. They are widely used as core sandwiches in sandwich structures due to their low density, light weight, low thermal conductivity and relatively high strength and stiffness. Because the wave absorbing performance of the gradient honeycomb wave absorbing material is far better than that of the uniform honeycomb wave absorbing material, the gradient honeycomb wave absorbing material has wider application in practice.
In practical project engineering, it is generally desirable to know equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, namely dielectric constant and magnetic permeability, and the electromagnetic performance of the material can be predicted through the equivalent electromagnetic parameters. But no equivalent electromagnetic parameter extraction method specially aiming at the gradient honeycomb wave-absorbing material exists at present.
In materials science, a common electromagnetic parameter extraction method is the NRW method. The method directly utilizes the reflection coefficient and the transmission coefficient of the electromagnetic wave after the electromagnetic wave is incident on the object to calculate the equivalent electromagnetic parameter, but has the limit condition that the height of the material is far less than the wavelength. For the gradient honeycomb wave-absorbing material, the height of the material may be only slightly smaller than the wavelength, and the design of a unique gradient coating structure is provided, which can reduce the impedance mismatch. Therefore, the equivalent electromagnetic parameters of the gradient cellular wave-absorbing material obtained by directly using the NRW method cannot be accurately calculated and used subsequently, and therefore an equivalent electromagnetic parameter extraction method considering the physical size parameters of the gradient structure is required, so that accurate equivalent electromagnetic parameters are obtained. The electromagnetic property of the gradient honeycomb wave-absorbing material can be directly calculated through the equivalent parameters, so that the application possibility of the material can be rapidly predicted.
Disclosure of Invention
Aiming at the problems or the defects, the problem that the obtained equivalent electromagnetic parameters are inaccurate due to the fact that the physical size parameters of the specific gradient structure in the existing equivalent electromagnetic parameter extraction method are not considered is solved. The invention provides an equivalent electromagnetic parameter extraction method of a gradient honeycomb wave-absorbing material.
The specific technical scheme is as follows:
step 1, obtaining scattering parameters S of the gradient honeycomb wave-absorbing material by using electromagnetic simulation software CST, wherein S comprises S11And S21
Firstly, drawing a gradient honeycomb wave-absorbing material model in electromagnetic simulation software CST, then setting periodic unit boundary conditions to enable electromagnetic waves to be vertically incident along the positive gradient direction of a coating, and carrying out frequency domain simulation in 2-18GHz to obtain scattering parameters S, wherein S comprises11And S21
Step 2, deducing NRW method equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material by using the S parameters according to a transmission line theory and a microwave theory, solving the multivalue problem by using an imaginary part phase compensation method, and obtaining preliminary equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, wherein the method specifically comprises the following steps:
according to the transmission line theory and the microwave theory, the scattering coefficients between two ports of the gradient honeycomb wave-absorbing material can be respectively expressed as follows:
S11=S22=(1-T2)Γ/(1-Γ2T2) (1)
S21=S12=(1-Γ2)T/(1-Γ2T2)(2)
wherein Γ ═ Z (Z)s-Zo)/(Zs+Zo) For electromagnetic waves from air (impedance Z)o) Perpendicular projection onto an infinitely thick medium (relative dielectric constant ε)rRelative magnetic permeability murImpedance of
Figure BDA0002364435060000021
) Reflection coefficient at surface, T ═ exp (jk)0nl) is the transmission coefficient of electromagnetic waves in the gradient honeycomb wave-absorbing material with the thickness of l, and k0ω/c is the wave vector of the electromagnetic wave in vacuum,
Figure BDA0002364435060000022
is the refractive index of the gradient honeycomb wave-absorbing material. Order to
V1=S21+S11(3)
V2=S21-S11(4)
Figure BDA0002364435060000023
The reflection coefficient Γ and the propagation coefficient T may be expressed as
Figure BDA0002364435060000024
Figure BDA0002364435060000025
Is formed by gamma-L (Z)s-Zo)/(Zs+Zo) And T ═ exp (jk)0nl), and order
Figure BDA0002364435060000026
The following can be obtained:
Figure BDA0002364435060000027
Figure BDA0002364435060000028
through Z'sThe expression of n can be used to obtain the scattering coefficient of the measured
Figure BDA0002364435060000029
And
Figure BDA00023644350600000210
the relation between the two can further obtain the equivalent magnetic permeability mu of the NRW method of the gradient honeycomb wave-absorbing materialrAnd NRW equivalent dielectric constant εrAs follows:
μr=Z′sn (10)
εr=n/Z′s(11)
from the above formula (9)
Figure BDA00023644350600000211
Since ln (t) has multiple solutions (as shown in equations (12) and (13), there are infinite solutions for the refractive index, which in turn makes the electromagnetic parameter solution inaccurate.
ln(T)=ln{|T|exp[j(θ±2nπ)]} (12)
ln(T)=ln(|T|)+j(θ±2nπ) (13)
Wherein n is 0, ± 1, ± 2.
The multivalue problem is caused by the phase difference of 2n pi, and the uncertainty of the phase, and is solved by using an imaginary phase compensation method. Imaginary phase compensation method: the main realization method is that ln (1/T) continuously rises with the increase of frequency f, so that n can be equal to 0, and when the frequency increases, the frequency is increased
Figure BDA0002364435060000031
Is less than the imaginary part
Figure BDA0002364435060000032
In the imaginary part of (1), n is replaced by n +1 to realize ln (1/T) phase compensation. Obtaining the initial equivalent magnetic conductivity mu of the gradient honeycomb wave-absorbing material after the imaginary part is correctedrAnd preliminary equivalent dielectric constant εr
Step 3, considering the influence of the gradient structure of the gradient honeycomb wave-absorbing material, and performing optimization calculation on the imaginary part of the preliminary equivalent dielectric constant to finally obtain the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, which specifically comprises the following steps:
the initial equivalent magnetic permeability mu is obtained after the calculation in the step 2rAnd preliminary equivalent dielectric constant εrBoth of which contain real and imaginary parts, i.e.:
μr=μ’-iμ” (14)
εr=ε’-iε” (15)
the obtained preliminary equivalent electromagnetic parameters are calculated only through S parameters, specific material height and gradient structures are not considered, different resonant frequency points and different loss intensities can be generated due to the difference of the material heights, and different impedance matching can be generated between the different gradient structures and air, so that the performance of electromagnetic wave absorption is influenced. Specifically, the coating of the gradient honeycomb wave-absorbing material which is firstly contacted by the electromagnetic waves is thin, and correspondingly, the impedance of the gradient honeycomb wave-absorbing material is close to that of air, so that more electromagnetic waves enter the gradient honeycomb wave-absorbing material. When the electromagnetic wave enters deeper positions, the coating of the gradient honeycomb wave-absorbing material is thicker, and the corresponding electromagnetic wave loss is larger and larger, so that more electromagnetic waves can be consumed in the gradient honeycomb wave-absorbing material. The imaginary part of the dielectric constant mainly represents the loss, so the imaginary part of the obtained preliminary equivalent dielectric constant needs to be calculated according to the gradient structure size
Figure BDA0002364435060000033
Wherein t isinRefers to the thickness of the coating, t, of the honeycomb at the incident end of the electromagnetic waveoutIs the thickness of the coating of the honeycomb at the emergent end of the electromagnetic wave, p is the number of gradient layers of the honeycomb, delta t is the thickness increment between adjacent gradient coatings, h is the total height of the gradient honeycomb, f is the frequency, epsilon0Is the dielectric constant in vacuum, mu0And (4) vacuum magnetic permeability. Then the formula (16) is substituted into the formulas (14) and (15) to obtain the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, namely
μe=μ’-iμ” (17)
Figure BDA0002364435060000041
The invention solves the multivalue problem by adopting an imaginary part phase compensation method; the influence of the unique gradient structure of the gradient honeycomb wave-absorbing material on equivalent parameters is considered, namely the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material can be extracted by mainly including the physical size parameters such as the coating thickness of an electromagnetic wave incident end, the coating thickness of an electromagnetic wave emergent end, the number of gradient layers of the gradient honeycomb wave-absorbing material, increment between adjacent gradient coatings and the like. The technical scheme of the invention has the advantages of simple principle and convenient use, and the obtained equivalent electromagnetic parameters are relatively accurate.
Drawings
FIG. 1 is a flow chart of the present invention;
FIG. 2a is a top view of a periodic structure of the gradient honeycomb wave-absorbing material, and FIG. 2b is a side sectional view of the periodic structure of the gradient honeycomb wave-absorbing material;
FIG. 3 is a schematic diagram of the periodic unit area of the gradient cellular wave-absorbing material calculated by the invention;
FIG. 4 is a graph of the dispersion dielectric constant values of the absorbing coatings of the examples;
FIG. 5 is a scattering parameter value obtained by software simulation of an embodiment;
FIG. 6 shows the equivalent electromagnetic parameters obtained by the embodiment;
FIG. 7 is a graph comparing the reflectivity calculated in the examples with the reflectivity simulated by the software and the reflectivity tested by the experiment.
Detailed Description
In order to further explain the invention and verify the correctness of the invention, a specific gradient honeycomb wave-absorbing material equivalent electromagnetic parameter extraction process and a physical test experiment and result are provided.
The flow chart is shown in fig. 1, and the steps specifically include:
step 1, obtaining scattering parameters S of the gradient honeycomb wave-absorbing material, including S11And S21. Drawing gradient honeycomb structure material in electromagnetic simulation software CST, setting periodic unit boundary conditions, vertically injecting electromagnetic wave along positive gradient direction of coating, and performing frequency domain simulation within 2-18GHz to obtain the final productTo scattering parameters S, including S11And S21. The method comprises the following specific steps:
the gradient honeycomb wave-absorbing material is composed of periodic structural units, and the top view and the side view are respectively shown in fig. 2a and fig. 2 b. As can be seen from the figure, the gradient honeycomb wave-absorbing Material is composed of three materials, namely a honeycomb substrate (Material 1 in fig. 2 b), a wave-absorbing coating (Material 2 in fig. 2 b) coated on the honeycomb substrate, and air (Material 3 in fig. 2 b). Because the coating is a gradient honeycomb wave-absorbing material, the coating is gradient.
To facilitate simulation, the present embodiment selects a gradient cell periodic cell as shown in fig. 3. The substrate material being a homogeneous isotropic material having an electromagnetic parameter epsilon11.6 and μ 11, the wall thickness w is 0.1mm, and the aperture side length r is 1.83 mm; the dielectric constant of the wave-absorbing coating is epsilon2Concrete real and imaginary values are shown in FIG. 4, and magnetic permeability μ 21, the gradient coating thickness is t1=12.5um,t2=25um,t337.5um, corresponding to each gradient coating height h1=h2=h36.67 cm; material 3 is set to air.
Establishing a gradient honeycomb wave-absorbing material periodic unit structure corresponding to the parameters in CST software, using unit cell periodic boundaries, automatically performing periodic continuation after setting, automatically generating Floquet boundary ports under the boundary condition, adding air boxes in the axial direction, and performing frequency domain simulation by using a time domain finite difference method to obtain scattering parameters, as shown in FIG. 5.
Step 2, deducing NRW method equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material by using the S parameters according to a transmission line theory and a microwave theory, solving the multivalue problem by using an imaginary part phase compensation method, and obtaining preliminary equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, wherein the steps are as follows:
the scattering coefficient between two ports of the homogeneous material can be expressed as:
S11=S22=(1-T2)Γ/(1-Γ2T2) (1)
S21=S12=(1-Γ2)T/(1-Γ2T2) (2)
wherein Γ ═ Z (Z)s-Zo)/(Zs+Zo) For electromagnetic waves from air (impedance Z)o) Perpendicular projection onto an infinitely thick medium (relative dielectric constant ε)rRelative magnetic permeability murImpedance of
Figure BDA0002364435060000051
) Reflection coefficient at surface, T ═ exp (jk)0nl) is the transmission coefficient of electromagnetic waves in the gradient honeycomb wave-absorbing material with the thickness of l, and k0ω/c is the wave vector of the electromagnetic wave in vacuum,
Figure BDA0002364435060000052
is the refractive index of the gradient honeycomb wave-absorbing material. Order to
V1=S21+S11(3)
V2=S21-S11(4)
Figure BDA0002364435060000053
The reflection coefficient Γ and the propagation coefficient T may be expressed as
Figure BDA0002364435060000054
Figure BDA0002364435060000055
Is formed by gamma-L (Z)s-Zo)/(Zs+Zo) And T ═ exp (jk)0nl), and order
Figure BDA0002364435060000061
The following can be obtained:
Figure BDA0002364435060000062
Figure BDA0002364435060000063
through Z'sThe expression of n can be used to obtain the scattering coefficient of the measured
Figure BDA0002364435060000064
And
Figure BDA0002364435060000065
the relation between the two can further obtain the equivalent magnetic permeability mu of the NRW method of the gradient honeycomb wave-absorbing materialrAnd NRW equivalent dielectric constant εrAs follows:
μr=Z′sn (10)
εr=n/Z′s(11)
from the above formula (9)
Figure BDA0002364435060000066
Since ln (t) has multiple solutions (as shown in equations (12) and (13)), there are infinite solutions for the refractive index, which in turn makes the electromagnetic parameter solution inaccurate.
ln(T)=ln{|T|exp[j(θ±2nπ)]} (12)
ln(T)=ln(|T|)+j(θ±2nπ) (13)
Wherein n is 0, ± 1, ± 2.
The multivalue problem is caused by the phase difference of 2n pi, and the uncertainty of the phase, and is solved by using an imaginary phase compensation method. The main implementation method of the imaginary part phase compensation method is that ln (1/T) continuously rises with the increase of the frequency f, so that the method can start from n being 0, and when the frequency increases, the imaginary part phase compensation method
Figure BDA0002364435060000067
Is less than the imaginary part
Figure BDA0002364435060000068
In the imaginary part of (1), n is changed from n +1Ln (1/T) phase compensation is implemented instead. Obtaining the initial equivalent magnetic permeability mu of the medium after the imaginary part is correctedrAnd preliminary equivalent dielectric constant εr
And 3, considering the influence of the gradient structure of the gradient honeycomb wave-absorbing material, and performing optimization calculation on the imaginary part of the primary equivalent dielectric constant to finally obtain the integral equivalent electromagnetic parameters of the gradient honeycomb material.
The initial equivalent magnetic permeability mu is obtained after the calculation in the step 2rAnd the equivalent dielectric constant εrBoth of which contain real (μ ', ε') and imaginary (μ ", ε") parts, namely:
μr=μ’-iμ” (14)
εr=ε’-iε” (15)
the obtained preliminary equivalent electromagnetic parameters are calculated only by the S parameters, the specific material height and the gradient structure are not considered, the influence of the gradient structure on the equivalent electromagnetic parameters is considered, and the calculation is carried out according to the following formula, wherein t is the equation in the embodimentout=37.5um,tin=12.5um,P=3,Δt=12.5um,h=20um。
Figure BDA0002364435060000071
Then the formula (16) is substituted into the formulas (14) and (15) to obtain the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, namely
μe=μ’-iμ” (17)
Figure BDA0002364435060000072
The equivalent electromagnetic parameters of the gradient cellular wave-absorbing material calculated by using the formula (17) and the formula (18) are shown in fig. 6, where fig. 6a is the real part of the equivalent electromagnetic parameters, and fig. 6b is the imaginary part of the equivalent electromagnetic parameters.
And then preparing a gradient honeycomb wave-absorbing material object, and testing the reflectivity by using an arch frame reflectivity testing system. Meanwhile, simulating the gradient honeycomb wave-absorbing material by using CST software to obtain the reflectivity, and calculating the reflectivity by using the equivalent parameters of the invention. Three reflectivities obtained by actually measuring the gradient honeycomb wave-absorbing material, simulating CST software and calculating by the method are shown in figure 7, and the reflectivities obtained by 3 methods are consistent within 2-18GHz, which shows that the method has reliability.

Claims (1)

1. An equivalent electromagnetic parameter extraction method of a gradient honeycomb wave-absorbing material comprises the following steps:
step 1, obtaining scattering parameters S of the gradient honeycomb wave-absorbing material by using electromagnetic simulation software CST, wherein S comprises S11And S21
Firstly, drawing a gradient honeycomb wave-absorbing material model in electromagnetic simulation software CST, then setting periodic unit boundary conditions to enable electromagnetic waves to be vertically incident along the positive gradient direction of a coating, and carrying out frequency domain simulation in 2-18GHz to obtain scattering parameters S, wherein S comprises11And S21
Step 2, deducing NRW method equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material by using the S parameters according to a transmission line theory and a microwave theory, solving the multivalue problem by using an imaginary part phase compensation method, and obtaining preliminary equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, wherein the method specifically comprises the following steps:
according to the transmission line theory and the microwave theory, the scattering coefficients between two ports of the gradient honeycomb wave-absorbing material can be respectively expressed as follows:
S11=S22=(1-T2)Γ/(1-Γ2T2) (1)
S21=S12=(1-Γ2)T/(1-Γ2T2) (2)
wherein Γ ═ Z (Z)s-Zo)/(Zs+Zo) For electromagnetic waves by impedance ZoWhen the air is vertically projected to the surface of an infinitely thick medium; relative dielectric constant epsilon of infinitely thick mediarRelative magnetic permeability murImpedance of
Figure FDA0002364435050000011
T=exp(jk0nl) is the transmission coefficient of electromagnetic waves in the gradient honeycomb wave-absorbing material with the thickness of l, and k0ω/c is the wave vector of the electromagnetic wave in vacuum,
Figure FDA0002364435050000012
the refractive index of the gradient honeycomb wave-absorbing material; order to
V1=S21+S11(3)
V2=S21-S11(4)
Figure FDA0002364435050000013
The reflection coefficient Γ and the propagation coefficient T may be expressed as
Figure FDA0002364435050000014
Figure FDA0002364435050000015
Is formed by gamma-L (Z)s-Zo)/(Zs+Zo) And T ═ exp (jk)0nl), and order
Figure FDA0002364435050000016
The following can be obtained:
Figure FDA0002364435050000017
Figure FDA0002364435050000021
through Z'sAnd n is expressed to obtain the scattering coefficient of the measured
Figure FDA0002364435050000022
And
Figure FDA0002364435050000023
further obtains the equivalent magnetic permeability mu of the NRW method of the gradient honeycomb wave-absorbing materialrAnd NRW equivalent dielectric constant εrAs follows:
μr=Z'sn (10)
εr=n/Z's(11)
imaginary phase compensation method: since ln (1/T) continuously increases with the increase of the frequency f, starting from n equal to 0, when the frequency increases
Figure FDA0002364435050000024
Is less than the imaginary part
Figure FDA0002364435050000025
When n is replaced by n +1, ln (1/T) phase compensation is realized; the imaginary part is corrected by using an imaginary part phase compensation method, and the equivalent electromagnetic parameter after the imaginary part is corrected is called as the initial equivalent magnetic conductivity mu of the gradient honeycomb wave-absorbing materialrAnd preliminary equivalent dielectric constant εr
Step 3, considering the influence of the gradient structure of the gradient honeycomb wave-absorbing material, and performing optimization calculation on the imaginary part of the preliminary equivalent dielectric constant to finally obtain the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, which specifically comprises the following steps:
the initial equivalent magnetic permeability mu obtained after the calculation in the step 2rAnd preliminary equivalent dielectric constant εrBoth of which contain real and imaginary parts, i.e.:
μr=μ'-iμ” (14)
εr=ε'-iε” (15)
the imaginary part of the obtained preliminary equivalent dielectric constant is calculated according to the gradient structure size as follows
Figure FDA0002364435050000026
Wherein t isinRefers to the thickness of the coating, t, of the honeycomb at the incident end of the electromagnetic waveoutIs the thickness of the coating of the honeycomb at the emergent end of the electromagnetic wave, p is the number of gradient layers of the honeycomb, delta t is the thickness increment between adjacent gradient coatings, h is the total height of the gradient honeycomb, f is the frequency, epsilon0Is the dielectric constant in vacuum, mu0Vacuum magnetic conductivity;
then the formula (16) is substituted into the formulas (14) and (15) to obtain the equivalent electromagnetic parameters of the gradient honeycomb wave-absorbing material, namely
μe=μ’-iμ” (17)
εe=ε’-iεe” (18)。
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CN112948980B (en) * 2021-03-31 2023-04-18 北京环境特性研究所 Electromagnetic scattering characteristic simulation modeling method and device of honeycomb wave-absorbing structure
CN113960512A (en) * 2021-11-03 2022-01-21 电子科技大学 Deduction calculation method for equivalent electromagnetic parameters of rubber plate type wave-absorbing material
CN113960512B (en) * 2021-11-03 2023-03-14 电子科技大学 Deduction calculation method for equivalent electromagnetic parameters of rubber plate type wave-absorbing material

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