CN116796541A - Rapid design method of ultra-wideband metamaterial wave absorber - Google Patents
Rapid design method of ultra-wideband metamaterial wave absorber Download PDFInfo
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Abstract
The invention discloses a rapid design method of an ultra-wideband metamaterial absorber, which is suitable for the metamaterial absorber consisting of a high-resistance surface, a dielectric plate and a metal plate. In the invention, the equivalent dielectric constant of the high-resistance surface printed on the layered medium is deduced and used for establishing the accurate closing relation between the resistance, the capacitance and the design parameters of the wave absorber. Based on the transmission line theory, an equivalent circuit model of the absorber is established, and the optimal value of the lumped element of the target reflection parameter in the equivalent circuit model can be rapidly calculated by combining a genetic optimization algorithm. Then, the physical structure parameters of the wave absorber are obtained through the calculation of the closed expression. The invention can realize the rapid design of the ultra-wideband metamaterial wave absorber, save computing resources, shorten the design period and greatly improve the efficiency of the design of the metamaterial wave absorber.
Description
Technical Field
The invention relates to the technical field of metamaterial wave absorbers, in particular to a rapid design method of an ultra-wideband metamaterial wave absorber.
Background
The broadband wave-absorbing material is widely applied to the fields of electromagnetic shielding and electromagnetic stealth, and can dissipate and absorb the energy of the incident electromagnetic wave in a wider frequency range by utilizing a high-loss material and a strong resonance structure so as to achieve the stealth effect. The wave absorbing material is applied to the radar stealth field, and can greatly improve the burst prevention and striking capability and the battlefield survival capability of weapon equipment. The traditional wave-absorbing material has the limitations of large volume, large thickness and large density, and limits the application scene. The metamaterial has the artificial composite structure and the composite material with the extraordinary physical properties which are not possessed by the natural material, the metamaterial wave absorber can overcome the thickness limitation of the traditional wave absorbing material, has the advantages of small volume, thin thickness and light weight, and has great potential application value in the stealth field.
However, when the traditional design method of the metamaterial absorber optimizes design parameters, full-wave simulation needs to be operated for multiple times to meet the wave absorbing target, so that the problems of long design period, waste of calculation resources and the like are caused, and the finding of a rapid and simple method for designing the broadband metamaterial absorber has important research significance. In the rapid design method of the metamaterial wave absorber, the accurate equivalent dielectric constant is a key link in the rapid design process. However, the existing research is seldom focused on the precise equivalent dielectric constant of the layered medium, and is applied to the design of the ultra-wideband metamaterial wave absorber. In addition, the absorption bandwidth of the metamaterial wave absorber designed by the existing rapid design method still needs to be expanded to low frequency and high frequency so as to meet the broadband stealth requirement.
Disclosure of Invention
In order to rapidly and accurately design the ultra-wideband metamaterial absorber with ultra-wideband absorption performance, the invention provides a rapid design method of the ultra-wideband metamaterial absorber, which reduces the waste of computing resources and improves the design efficiency.
In order to achieve the technical purpose, the invention adopts the following technical scheme:
a rapid design method of an ultra-wideband metamaterial wave absorber comprises the following steps:
s1: setting target reflection parameters of the metamaterial wave absorber according to the design requirements of the metamaterial wave absorber;
s2: according to the structural characteristics of the metamaterial wave absorber, an equivalent circuit model of the metamaterial wave absorber is built based on a transmission line theory;
s3: establishing a closed expression of resistance and capacitance in the metamaterial wave absorber structure type and equivalent circuit model according to the equivalent relation in the step S2;
s4: according to the closed expression, combining an optimization algorithm and an equivalent circuit model, rapidly optimizing to obtain optimal values of resistance and capacitance in the equivalent circuit model, and further calculating structural parameters of the metamaterial absorber;
s5: and designing an ultra-wideband metamaterial wave absorber meeting the target frequency range and reflection loss according to the structure type and the structure parameters.
Compared with the prior art, the invention has the beneficial effects that:
(1) Establishing an accurate closing relationship between the circuit model and the physical structure of the wave absorber by deducing the accurate equivalent dielectric constant of the high-resistance surface printed on the layered medium; (2) The optimal value of the circuit element meeting the target performance can be obtained rapidly from the circuit angle, and further the physical structure parameter of the wave absorber is obtained through the calculation of the closed relation, so that the defect of repeated iterative optimization of the full-wave simulation software is avoided, and the design time and calculation resources are saved greatly; (3) The whole thickness of the ultra-wideband metamaterial wave absorber designed based on the method is close to the theoretical minimum thickness.
Drawings
For a clearer description of embodiments of the invention or of the prior art, the drawings which are used in the description of the embodiments or of the prior art will be briefly described, it being evident that the drawings in the description below are only some embodiments of the invention, and that other drawings can be obtained according to these drawings without inventive effort for a person skilled in the art.
FIG. 1 is a flow chart of the method of the present invention.
Fig. 2 is a diagram of a physical structure model of an n-layer ultra-wideband metamaterial absorber.
Fig. 3 is a model diagram of an equivalent circuit of an n-layer ultra-wideband metamaterial absorber.
FIG. 4 is a graph of the equivalent permittivity versus dielectric substrate and interlayer permittivity for an example.
Fig. 5 is a schematic view of an ultra wideband metamaterial absorber designed in an embodiment.
FIG. 6 is a graph showing the comparison between the full-wave simulation result and the equivalent circuit result in the embodiment.
In the figure: 0. a metal plate; 1. a high-resistance surface with length of w1 and sheet resistance of Rs 1; 2. a high-resistance surface with length of w2 and sheet resistance of Rs 2; 3. a high-resistance surface with length of w3 and sheet resistance of Rs 3; 4. a high-resistance surface with length of w4 and sheet resistance of Rs 4; 5. a high-resistance surface with length of w5 and sheet resistance of Rs 5; 6. a high-resistance surface with length of w6 and sheet resistance of Rs 6; 7. a high-resistance surface with length of w7 and sheet resistance of Rs 7; 8. a polyethylene terephthalate (PET) dielectric substrate having a thickness hs; 9. the thickness of the medium layers is respectively h1, h2, h3, h4, h5, h6 and h7, namely a Polymethacrylimide (PMI) medium interlayer.
Detailed Description
The following describes the embodiments of the present invention further with reference to the drawings.
As shown in FIG. 1, the method for rapidly designing the ultra-wideband metamaterial wave absorber comprises the following steps:
s1: setting target reflection parameters of the metamaterial wave absorber according to the design requirements of the metamaterial wave absorber; the target reflection parameters include the frequency range and the reflection loss, and in this embodiment, the target reflection performance is set to be 0.5GHz-90GHz, and the internal reflection parameter is lower than-10 dB. According to the target reflection performance, the metamaterial wave absorber adopts an n=7-layer structure, the dielectric substrate adopts a PET material, the dielectric constant is 3, the loss tangent is 0.06, the thicknesses are all 0.125mm, and in order to obtain the large working bandwidth, the dielectric interlayer adopts PMI foam, the dielectric constant is 1.05, and the loss tangent is 0.005.
S2: FIG. 2 is a physical model of an n-layer metamaterial absorber, the ultra-wideband metamaterial absorber comprising a square high-resistance surface, a dielectric substrate for printing the high-resistance surface, a dielectric interlayer and a metal plate, wherein the dielectric interlayer has a dielectric constant smaller than that of the dielectric substrate; according to the structural characteristics of the metamaterial wave absorber, the n-layer metamaterial wave absorber physical model shown in the figure 2 is equivalent to an equivalent circuit model shown in the figure 3 based on a transmission line theory; in the equivalent circuit model, the square high-resistance surface is equivalent to a resistor and capacitor series circuit, and the dielectric layer is equivalent to a transmission line with the same length as the resistor and capacitor series circuit; according to the transmission line theory, an expression of a reflection parameter coefficient gamma and input impedance is obtained:
Z′ 1 ＝jZ r，1 tan(β r，1 d 1 )
wherein Z is HIS，i Impedance of the i-th square high-resistance surface, Z' 1 Is the input impedance at the interlayer of the first dielectric layer, Z' i Z is the input impedance at the interlayer of the ith dielectric layer in，i Z is the input impedance of the ith layer of absorber in Z is the input impedance 0 =377Ω is the free space impedance,and->The specific impedance of the i-th dielectric substrate and the dielectric interlayer are respectively +.>And->Is a phase constant; ri and Ci are lumped elements of the ith layer; d, d i And d s，i The thickness of the dielectric interlayer of the i-th layer and the thickness of the dielectric substrate are respectively;
then, the input impedance of the n-layer absorber can be calculated by the following equation:
s3: establishing a closed expression of resistance and capacitance in the metamaterial wave absorber structure type and equivalent circuit model according to the equivalent relation in the step S2; the square high-resistance surface can be equivalently an RC series circuit, and the closed expression of the resistor and the capacitor in the equivalent circuit model is as follows:
wherein R is i Is a square high-resistance surface equivalent resistance, C i Is a square high-resistance surface equivalent capacitor, R s，i Is the square resistance value of the i-th layer square high-resistance surface, S is the surface area of the metamaterial wave absorber unit structure, A i Is the surface area of the ith square resistor film, C 0 Is the extraction capacitance epsilon of square resistance film eff，i Is the equivalent dielectric constant of the ith layer epsilon 0 The vacuum dielectric constant, g is the gap between the adjacent high-resistance surfaces, and p is the period length of the metamaterial wave absorber unit structure;
ε eff，i the calculation method comprises the following steps:
wherein ε r，i And epsilon s，i The dielectric constant of the dielectric interlayer of the ith layer and the dielectric constant of the dielectric substrate respectively, d i And d s，i Respectively the thickness of the i-th dielectric interlayer and the thickness of the dielectric substrate epsilon r，i+1 The dielectric constant of the dielectric interlayer of the (i+1) th layer, d i+1 Is the (i+1) th layer mediumThe thickness of the interlayer, alpha is the shape factor, p is the period of the metamaterial wave absorber unit structure, epsilon av，i The high-resistance surface of the ith layer is clamped between the dielectric interlayer of the (i+1) th layer and the dielectric substrate of the ith layer; epsilon rd，i An average dielectric constant of the i-th layer high-resistance surface;
calculating to obtain d s，i ＝0.125mm，ε r，i Equivalent dielectric constant of =1.05 with d i And epsilon s，i A changing situation.
S4: according to the closed expression, combining an optimization algorithm and an equivalent circuit model, rapidly optimizing to obtain optimal values of resistance and capacitance in the equivalent circuit model, and further calculating structural parameters of the metamaterial absorber; the structural parameters of the metamaterial wave absorber comprise: the thickness of the medium interlayer, the square resistance value of the high-resistance surface, the length of the high-resistance surface and the period of the unit structure.
In order to reduce the number of optimization parameters, the unit structure period p=32mm is determined, and the optimization parameters are the sheet resistance R of the high-resistance surface s，i Length wi, and thickness hi of the dielectric interlayer, where i=1, 2,3 … 7.
And then combining a genetic optimization algorithm and an equivalent circuit model to perform iterative optimization, and setting a difference between the current iteration and a target of fitness function evaluation, wherein the difference is expressed as follows:
where i represents the ith optimization objective, wi is a weight factor, ni and fj are the number of frequencies in the frequency range and the jth frequency point, ri (fj) and Gi (fj) are the iterative reflection parameter and the target reflection parameter, respectively, and m is the target number.
After a certain number of iterations to meet the fitness function, the optimal values of lumped elements in the equivalent circuit model can be obtained, wherein the optimal values are r1=282.7Ω, r2=372.2Ω, r3= 987.7 Ω, r4= 874.9 Ω, r5=1245Ω, r6=1022 Ω and r7=1654Ω respectively; c1 70.36pF, c2=26.52 pF, c3=53.88 pF, c4=23.96 pF, c5=14.25 pF, c6=13.94 pF, c7=14.98 pF.
Then, according to the closed relation between the equivalent lumped element and the absorber structure parameter, calculating to obtain the optimal value of the absorber physical structure parameter meeting the target reflection parameter:
Rs1＝282.7Ω/□，Rs2＝372.2Ω/□，Rs3＝987.7Ω/□，Rs4＝874.9Ω/□，Rs5＝1245Ω/□，Rs6＝1022Ω/□，Rs7＝1654Ω/□。
w1=31.5 mm; w2=26.9 mm; w3=30.8 mm; w4=26.1 mm; w5=21.9 mm; w6=21.7 mm; w7=18.7 mm; d1=14.8 mm; d2 =7mm; d3 =8.8 mm; d4 =4.3 mm; d5 =3mm; d6 =2.8mm; d7 =1.1 mm. The ultra-wideband metamaterial absorber is shown in figure 5.
S5: and designing an ultra-wideband metamaterial wave absorber meeting the target frequency range and reflection loss according to the structure type and the structure parameters.
According to the calculated optimal value of the physical structure parameter of the metamaterial wave absorber, modeling simulation is carried out in full-wave simulation software, a wave absorber structure model is shown in fig. 5, consistency of a circuit optimization result and a full-wave simulation result is verified, comparison results of the two are shown in fig. 6, reflection parameters of the wave absorber are below-10 dB within 0.72GHz-92GHz, curves of the two are consistent, and the advantages of effectiveness and accuracy of the rapid design method are illustrated.
Furthermore, according to the Rozanov limit, the minimum theoretical thickness expression for a non-magnetic absorber is:
where ρ (λ) and Γ (λ) are functions of reflection parameters in linear and dB form with respect to wavelength. The minimum theoretical thickness of the metamaterial wave absorber designed according to calculation is 40.11mm, the designed thickness is 42.67mm, and the minimum theoretical thickness of the metamaterial wave absorber and the designed thickness are very close. The design method of the ultra-wideband wave absorber of the metamaterial provided by the invention can rapidly and accurately design and realize any ultra-wideband wave absorber by deducing the accurate equivalent dielectric constant and combining an equivalent circuit model and a genetic algorithm, and the overall thickness of the ultra-wideband wave absorber is close to the theoretical minimum thickness, so that the calculation resources and the design time can be greatly saved.
The foregoing is merely illustrative of the present invention, and the present invention is not limited thereto, and any person skilled in the art will readily recognize that variations or substitutions are within the scope of the present invention. Therefore, the protection scope of the present invention shall be subject to the protection scope of the claims.
Claims (6)
1. The rapid design method of the ultra-wideband metamaterial wave absorber is characterized by comprising the following steps of:
s1: setting target reflection parameters of the metamaterial wave absorber according to the design requirements of the metamaterial wave absorber;
s2: according to the structural characteristics of the metamaterial wave absorber, an equivalent circuit model of the metamaterial wave absorber is built based on a transmission line theory;
s3: establishing a closed expression of resistance and capacitance in the metamaterial wave absorber structure type and equivalent circuit model according to the equivalent relation in the step S2;
s4: according to the closed expression, combining an optimization algorithm and an equivalent circuit model, rapidly optimizing to obtain optimal values of resistance and capacitance in the equivalent circuit model, and further calculating structural parameters of the metamaterial absorber;
s5: and designing an ultra-wideband metamaterial wave absorber meeting the target frequency range and reflection loss according to the structure type and the structure parameters.
2. The method according to claim 1, wherein the target reflection parameters in step S1 include a frequency range and a reflection loss.
3. The method for rapidly designing an ultra-wideband metamaterial absorber according to claim 1, wherein in the equivalent circuit model in the step S2, the square high-resistance surface is equivalent to a series circuit of resistor and capacitor, and the dielectric layer is equivalent to a transmission line with the same length.
4. The method for rapidly designing an ultra wideband metamaterial absorber according to claim 1, wherein the closed expression of the resistor and the capacitor in the equivalent circuit model in the step S3 is as follows:
C i ＝ε eff,i C 0 ；
wherein R is i Is a square high-resistance surface equivalent resistance, C i Is a square high-resistance surface equivalent capacitor, R s,i Is the square resistance value of the i-th layer square high-resistance surface, S is the surface area of the metamaterial wave absorber unit structure, A i Is the surface area, w, of the ith square resistor film i Is the length of the i-th layer resistance film, C 0 Is the extraction capacitance epsilon of square resistance film eff,i Is the equivalent dielectric constant of the i-th layer.
5. The method for rapidly designing an ultra-wideband metamaterial absorber according to claim 4, wherein epsilon eff,i The calculation method comprises the following steps:
wherein ε r,i And epsilon s,i The dielectric constant of the dielectric interlayer of the ith layer and the dielectric constant of the dielectric substrate respectively, d i And d s,i Respectively the thickness of the i-th dielectric interlayer and the thickness of the dielectric substrate epsilon r,i+1 The dielectric constant of the dielectric interlayer of the (i+1) th layer, d i+1 Is the (i+1) th layer mediumThe thickness of the interlayer, alpha is the shape factor, p is the period length of the metamaterial wave-absorbing unit structure, epsilon av,i The high-resistance surface of the ith layer is clamped between the dielectric interlayer of the (i+1) th layer and the dielectric substrate of the ith layer; epsilon rd,i The average dielectric constant of the i-th layer high-resistance surface.
6. The method for rapidly designing an ultra-wideband metamaterial absorber according to claim 1, wherein the structural parameters of the metamaterial absorber in step S4 include: the thickness of the medium interlayer, the square resistance value of the high-resistance surface, the length of the high-resistance surface and the period of the unit structure.
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