Frequency selective surface wave transmission analysis method based on equivalent medium model

Abstract

The application provides a frequency selective surface wave transmission analysis method based on an equivalent medium model, comprising the following steps: equivalent to a medium model; obtaining a vertical incidence transmission coefficient and a vertical incidence reflection coefficient of an electromagnetic wave vertically incident on the frequency selective surface; and calculating the transmission coefficient and the reflection coefficient of the electromagnetic wave incident on the frequency selective surface at an arbitrary incidence angle, so as to simplify the wave transmission analysis process of the frequency selective surface, ensure the wave transmission analysis precision, and greatly reduce the calculation process and time.

Description

Technical Field

[0001] This invention relates to the field of frequency selective surface technology, and more particularly to a frequency selective surface transmission analysis method based on an equivalent medium model. Background Technology

[0002] A frequency selective surface typically refers to an infinite array of identical metal patch units or perforated units on a metal screen, arranged periodically along a one-dimensional or two-dimensional direction. It is selective for the frequency, polarization, and incident angle of the incident electromagnetic wave, and is equivalent to an open-space electromagnetic wave filter.

[0003] Frequency selective surfaces (FSTs) are commonly used to synthesize artificial impedance surfaces and electromagnetic bandgap surfaces, enhancing the electrical performance of various microwave devices, including antennas and electromagnetic absorbers. They have wide applications in wireless communication, electromagnetic shielding, and radar stealth. Taking radar stealth as an example, it heavily relies on accurately acquiring the transmission characteristics of FSTs. Given that the incident angle of electromagnetic waves is arbitrary, how to quickly and accurately perform transmission analysis on FSTs at arbitrary incident angles is a crucial problem that needs to be solved in engineering applications.

[0004] Based on this need, many wave transmission analysis methods have been proposed, including full-wave methods and approximation methods. Full-wave methods include the finite-difference time-domain method, the method of moments, and the finite element method. These methods employ rigorous vector solutions and can obtain accurate electromagnetic characteristics of the frequency-selective surface, but they are computationally expensive. Approximation methods include equivalent circuit methods and multimode equivalent network methods. These methods equate the frequency-selective surface to capacitors and inductors, offering advantages such as short computation time and clear physical meaning, but the computation and modeling processes are more complex.

[0005] To address the aforementioned problems, this invention proposes a frequency-selective surface transmission analysis method based on an equivalent medium model. Summary of the Invention

[0006] To address the aforementioned technical problem of time-consuming frequency-selective surface analysis, this invention provides a frequency-selective surface transmission analysis method based on an equivalent medium model. This invention primarily treats the frequency-selective surface as an equivalent medium model, obtaining the surface thickness, the perpendicular incident transmission coefficient, and the perpendicular incident reflection coefficient of electromagnetic waves incident on the frequency-selective surface. Through calculation, the transmission and reflection coefficients of electromagnetic waves incident on the frequency-selective surface at any incident angle are obtained. This significantly reduces the modeling and calculation time of the frequency-selective surface while maintaining the accuracy of the transmission analysis. The technical means employed in this invention are as follows:

[0007] This invention provides a frequency-selective surface transmission wave analysis method based on an equivalent medium model, comprising:

[0008] Provides a frequency-selective surface with uniform thickness;

[0009] The frequency selection surface is equivalent to a dielectric model, which is a plate of uniform material. The dielectric model has the same thickness as the frequency selection surface, and the outer contour of the dielectric model is the same as the outer contour of the frequency selection surface.

[0010] Obtain the perpendicular incident transmission coefficient and perpendicular incident reflection coefficient of electromagnetic waves incident perpendicularly on the frequency-selective surface;

[0011] The wave impedance and complex refractive index of the medium model are obtained based on the perpendicular incident transmission coefficient and the perpendicular incident reflection coefficient.

[0012] The permeability and dielectric constant of the medium model are obtained based on the wave impedance and the complex refractive index.

[0013] By selecting the incident angle of the electromagnetic wave, the wave vector of the medium model at the incident angle is obtained based on the incident angle, the magnetic permeability, and the dielectric constant.

[0014] Based on the wave vector of the medium model at the incident angle, the transmission matrix of the medium model at the incident angle is obtained.

[0015] Based on the transmission matrix of the medium model at the incident angle, the transmission coefficient and reflection coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle are obtained.

[0016] Furthermore, the wave impedance is calculated as follows:

[0017]

[0018] Where z is the wave impedance, S 11 ’ S is the vertical incident reflection coefficient. 21 ’ The vertical incident transmission coefficient is denoted as .

[0019] Furthermore, the complex refractive index is calculated as follows:

[0020]

[0021] Wherein, n is the complex refractive index, k0 is the wave vector in free space, and d is the thickness of the medium model.

[0022] Furthermore, the sign of the wave impedance of the medium model is determined by the real part of the wave impedance, and the sign of the complex refractive index of the medium model is determined by the imaginary part of the complex refractive index.

[0023] Furthermore, the permeability is calculated as follows:

[0024] μ = nz;

[0025] Where μ is the magnetic permeability, n is the complex refractive index, and z is the wave impedance.

[0026] Furthermore, the dielectric constant is calculated in the following manner:

[0027]

[0028] Wherein, ε is the dielectric constant, n is the complex refractive index, and z is the wave impedance.

[0029] Further, the wave vector of the dielectric model at the incident angle, obtained based on the incident angle, the permeability, and the dielectric constant, is calculated in the following manner:

[0030]

[0031] Wherein, γ is the wave vector of the medium model at the incident angle, λ0 is the wavelength of the electromagnetic wave, ε is the dielectric constant, μ is the permeability, and θ is the incident angle.

[0032] Furthermore, based on the wave vector of the medium model at the incident angle, the transmission matrix of the medium model at the incident angle is obtained, and calculated in the following manner:

[0033]

[0034] Where j is an imaginary number, γ is the wave vector of the medium model at the incident angle, d is the thickness of the medium model, z is the wave impedance, ch is a hyperbolic cosine function, sh is a hyperbolic sine function, and A, B, C, and D are elements of the transmission matrix of the medium model at the incident angle.

[0035] Furthermore, the transmission coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle is calculated as follows:

[0036]

[0037] Among them, S 21 Z0 is the transmission coefficient of the surface selected when the electromagnetic wave is incident at the frequency at the incident angle, and Z0 is the characteristic impedance of free space, Z0 = 120π.

[0038] Furthermore, the reflection coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle is calculated as follows:

[0039]

[0040] Among them, S 11 Let Z0 be the reflection coefficient of the surface selected when the electromagnetic wave is incident at the frequency at the incident angle, and Z0 be the characteristic impedance of free space, Z0 = 120π.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] The frequency-selective surface transmission analysis method based on an equivalent dielectric model provided by this invention equates the frequency-selective surface to a dielectric model, where the dielectric model is a plate of uniform material with the same thickness and outer contour as the frequency-selective surface. The method obtains the perpendicular incident transmission coefficient and perpendicular incident reflection coefficient of the electromagnetic wave incident on the frequency-selective surface; derives the wave impedance and complex refractive index of the dielectric model based on the perpendicular incident transmission coefficient and the complex refractive index; derives the permeability and dielectric constant of the dielectric model based on the wave impedance and complex refractive index; selects the incident angle of the electromagnetic wave; and obtains the wave vector of the dielectric model at the incident angle based on the incident angle, permeability, and dielectric constant; derives the transmission matrix of the dielectric model at the incident angle based on the wave vector of the dielectric model at the incident angle; and obtains the transmission coefficient and reflection coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle based on the transmission matrix of the dielectric model at the incident angle. The frequency selective surface transmission analysis method based on the equivalent medium model provided by this invention can calculate the transmission coefficient and reflection coefficient of a frequency selective surface incident at any angle, simplifying the transmission analysis process of the frequency selective surface. While ensuring the accuracy of the transmission analysis, it avoids modeling the radome loaded on the frequency selective surface, greatly reducing the calculation process and time. Attached Figure Description

[0043] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0044] Figure 1 This is a flowchart of a frequency-selective surface transmission analysis method based on an equivalent medium model provided by the present invention.

[0045] Figure 2 This is a schematic diagram illustrating how the frequency-selective surface is equivalent to a dielectric model, as provided by the present invention.

[0046] Figure 3 A structural diagram of a frequency selective surface provided by the present invention.

[0047] Figure 4 for Figure 3 Enlarged view of point A in the middle.

[0048] Figure 5 This is a line graph of wave impedance versus frequency.

[0049] Figure 6 This is a line graph of complex refractive index versus frequency.

[0050] Figure 7 This is a line graph of permeability versus frequency.

[0051] Figure 8 This is a line graph of dielectric constant versus frequency.

[0052] Figure 9 A comparison chart showing the transmission and reflection coefficients calculated at different incident angles. Detailed Implementation

[0053] To enable those skilled in the art to better understand the present invention, the technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort should fall within the scope of protection of the present invention.

[0054] It should be noted that the terms "first," "second," etc., in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments of the invention described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" and "having," and any variations thereof, are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0055] Reference Figure 1 , Figure 2 , Figure 3 and Figure 4 , Figure 1 This is a flowchart of a frequency-selective surface transmission analysis method based on an equivalent medium model provided by the present invention. Figure 2 This is a schematic diagram illustrating how the frequency-selective surface is equivalent to a dielectric model, as provided by the present invention. Figure 3 This is a structural diagram of a frequency selective surface provided by the present invention. Figure 4 for Figure 3 The enlarged view at point A illustrates a specific embodiment of the frequency-selective surface transmission wave analysis method based on an equivalent medium model provided by this invention, including:

[0056] S1: Provides a frequency-selective surface with uniform thickness;

[0057] S2: The frequency selection surface is equivalent to a dielectric model, which is a plate with uniform material. The dielectric model has the same thickness as the frequency selection surface, and the outer contour of the dielectric model is the same as the outer contour of the frequency selection surface.

[0058] S3: Obtain the vertical incident transmission coefficient and vertical incident reflection coefficient of the electromagnetic wave vertical incident frequency-selective surface;

[0059] S4: Obtain the wave impedance and complex refractive index of the medium model based on the perpendicular incident transmission coefficient and the perpendicular incident reflection coefficient;

[0060] S5: Obtain the permeability and dielectric constant of the medium model based on the wave impedance and complex refractive index;

[0061] S6: Select the incident angle of the electromagnetic wave, and obtain the wave vector of the dielectric model at the incident angle based on the incident angle, magnetic permeability and dielectric constant.

[0062] S7: Based on the wave vector of the medium model at the incident angle, obtain the transmission matrix of the medium model at the incident angle;

[0063] S8: Based on the transmission matrix of the medium model at the incident angle, the transmission coefficient and reflection coefficient of the surface are selected by the incident frequency of the electromagnetic wave at the incident angle.

[0064] Understandably, in combination Figure 2 , Figure 3 and Figure 4 , Figure 4 Only one grid-shaped circular frequency selective surface topology is shown, where p = 9 mm, l = 7 mm, w1 = 0.2 mm, w2 = 0.2 mm, and the thickness of the grid-shaped circular frequency selective surface topology is d. The grid-shaped circular frequency selective surface topology array is arranged as shown below. Figure 3 A frequency-selective surface is shown. Figure 3 The frequency selection surface shown has a length and width of 3p-2w1 and a thickness of d; (Refer to...) Figure 2The frequency-selective surface is modeled as an equivalent dielectric model, with the same thickness and outer contour as the frequency-selective surface (i.e., the same dimensions). By treating the frequency-selective surface as an equivalent dielectric model, and knowing the perpendicular incident transmission coefficient and reflection coefficient of an electromagnetic wave incident perpendicularly on the frequency-selective surface, the transmission coefficient and reflection coefficient of an electromagnetic wave incident on the frequency-selective surface at any incident angle can be calculated. This simplifies the transmission analysis process of the frequency-selective surface, ensures the accuracy of the transmission analysis, and significantly reduces the calculation process and time.

[0065] In some alternative embodiments, reference continues to be made to... Figure 1 Wave impedance is calculated as follows:

[0066]

[0067] Where z is the wave impedance, S 11 ' is the reflection coefficient of perpendicular incidence, S 21 ' is the vertical incident transmission coefficient.

[0068] In some alternative embodiments, reference continues to be made to... Figure 1 The complex refractive index is calculated as follows:

[0069]

[0070] Where n is the complex refractive index, k0 is the wave vector in free space, and d is the thickness of the medium model.

[0071] In some alternative embodiments, refer to Figure 5 and Figure 6 , Figure 5 This is a line graph of wave impedance versus frequency. Figure 6 The graph is a line graph of complex refractive index versus frequency. The sign of the wave impedance in the medium model is determined by the real part of the wave impedance, and the sign of the complex refractive index in the medium model is determined by the imaginary part of the complex refractive index.

[0072] In some alternative embodiments, refer to Figure 7 , Figure 7 The graph shows the permeability versus frequency. Permeability is calculated as follows:

[0073] μ = nz;

[0074] Where μ is the magnetic permeability, n is the complex refractive index, and z is the wave impedance.

[0075] In some alternative embodiments, refer to Figure 8 , Figure 8 The graph shows the dielectric constant versus frequency. The dielectric constant is calculated as follows:

[0076]

[0077] Where ε is the dielectric constant, n is the complex refractive index, and z is the wave impedance.

[0078] In some alternative embodiments, reference continues to be made to... Figure 1 Based on the incident angle, permeability, and permittivity, the wave vector of the dielectric model at the incident angle is obtained, calculated as follows:

[0079]

[0080] Where γ is the wave vector of the medium model at the incident angle, λ0 is the wavelength of the electromagnetic wave, ε is the dielectric constant, μ is the permeability, and θ is the incident angle.

[0081] In some alternative embodiments, reference continues to be made to... Figure 1 Based on the wave vector of the medium model at the incident angle, the transmission matrix of the medium model at the incident angle is obtained, and calculated in the following manner:

[0082]

[0083] Where j is an imaginary number, γ is the wave vector of the medium model at the incident angle, d is the thickness of the medium model, z is the wave impedance, ch is a hyperbolic cosine function, sh is a hyperbolic sine function, and A, B, C, and D are the elements of the transmission matrix of the medium model at the incident angle.

[0084] In some alternative embodiments, reference continues to be made to... Figure 1 At the incident angle, the transmission coefficient of the surface is selected by the incident frequency of the electromagnetic wave, and is calculated as follows:

[0085]

[0086] Among them, S 21 Let Z0 be the transmission coefficient of the surface chosen by the incident frequency of the electromagnetic wave at the incident angle, and Z0 be the characteristic impedance of free space, Z0 = 120π.

[0087] In some alternative embodiments, reference continues to be made to... Figure 1 and Figure 9 , Figure 9 A comparison chart of the transmission and reflection coefficients at different incident angles is provided. The electromagnetic wave's reflection coefficient is selected based on the incident angle and frequency, and calculated as follows:

[0088]

[0089] Among them, S 11Let Z0 be the reflection coefficient of the surface chosen by the incident frequency of the electromagnetic wave at the incident angle, and Z0 be the characteristic impedance of free space, Z0 = 120π.

[0090] The sequence numbers of the above embodiments of the present invention are for descriptive purposes only and do not represent the superiority or inferiority of the embodiments.

[0091] In the above embodiments of the present invention, the descriptions of each embodiment have different focuses. For parts not described in detail in a certain embodiment, please refer to the relevant descriptions of other embodiments.

[0092] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, and not to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some or all of the technical features; and these modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A frequency-selective surface transmission wave analysis method based on an equivalent medium model, characterized in that, include: Provides a frequency-selective surface with uniform thickness; The frequency selection surface is equivalent to a dielectric model, which is a plate of uniform material. The dielectric model has the same thickness as the frequency selection surface, and the outer contour of the dielectric model is the same as the outer contour of the frequency selection surface. Obtain the perpendicular incident transmission coefficient and perpendicular incident reflection coefficient of electromagnetic waves incident perpendicularly on the frequency-selective surface; The wave impedance and complex refractive index of the medium model are obtained based on the perpendicular incident transmission coefficient and the perpendicular incident reflection coefficient. The permeability and dielectric constant of the medium model are obtained based on the wave impedance and the complex refractive index. By selecting the incident angle of the electromagnetic wave, the wave vector of the medium model at the incident angle is obtained based on the incident angle, the magnetic permeability, and the dielectric constant. Based on the wave vector of the medium model at the incident angle, the transmission matrix of the medium model at the incident angle is obtained. Based on the transmission matrix of the medium model at the incident angle, the transmission coefficient and reflection coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle are obtained.

2. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 1, characterized in that, The wave impedance is calculated as follows: Where z is the wave impedance, S 11 ' is the vertical incident reflection coefficient, S 21 ' is the vertical incident transmission coefficient.

3. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 2, characterized in that, The complex refractive index is calculated as follows: Wherein, n is the complex refractive index, k0 is the wave vector in free space, and d is the thickness of the medium model.

4. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 3, characterized in that, The sign of the wave impedance of the medium model is determined by the real part of the wave impedance, and the sign of the complex refractive index of the medium model is determined by the imaginary part of the complex refractive index.

5. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 1, characterized in that, The permeability is calculated as follows: μ = nz; Where μ is the magnetic permeability, n is the complex refractive index, and z is the wave impedance.

6. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 1, characterized in that, The dielectric constant is calculated as follows: Wherein, ε is the dielectric constant, n is the complex refractive index, and z is the wave impedance.

7. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 1, characterized in that, The wave vector of the dielectric model at the incident angle, obtained based on the incident angle, the permeability, and the dielectric constant, is calculated in the following manner: Wherein, γ is the wave vector of the medium model at the incident angle, λ0 is the wavelength of the electromagnetic wave, ε is the dielectric constant, μ is the permeability, and θ is the incident angle.

8. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 1, characterized in that, Based on the wave vector of the medium model at the incident angle, the transmission matrix of the medium model at the incident angle is obtained, and is calculated in the following manner: Where j is an imaginary number, γ is the wave vector of the medium model at the incident angle, d is the thickness of the medium model, z is the wave impedance, ch is a hyperbolic cosine function, sh is a hyperbolic sine function, and A, B, C, and D are elements of the transmission matrix of the medium model at the incident angle.

9. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 8, characterized in that, The transmission coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle is calculated as follows: Among them, S 21 Z0 is the transmission coefficient of the surface selected when the electromagnetic wave is incident at the frequency at the incident angle, and Z0 is the characteristic impedance of free space, Z0 = 120π.

10. The frequency-selective surface transmission wave analysis method based on an equivalent medium model according to claim 8, characterized in that, The reflection coefficient of the electromagnetic wave incident on the frequency-selective surface at the incident angle is calculated as follows: Among them, S 11 Let Z0 be the reflection coefficient of the surface selected when the electromagnetic wave is incident at the frequency at the incident angle, and Z0 be the characteristic impedance of free space, Z0 = 120π.

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