A non-uniform wave-absorbing material electromagnetic parameter inversion method based on an arch method test system

Abstract

The application discloses a non-uniform wave-absorbing material electromagnetic parameter inversion method based on a bow method test system, which comprises the following steps: step 1, deducing a mathematical formula for calculating electromagnetic parameters through reflectivity; step 2, a reflectivity test method and process; and step 3, performing electromagnetic parameter inversion of the non-uniform wave-absorbing material. Compared with a traditional transmission / reflection measurement method, the method does not need to precisely cut and process the sample in the test process, and does not damage the microstructure of the material to be measured. In the inversion algorithm, the reflectivity amplitude inversion method is adopted by using the dual polarization and oblique incidence reflectivity data, and compared with the NRW method, the multi-solution problem caused by the phase ambiguity is avoided. The method can more accurately calibrate the parameters of the non-uniform wave-absorbing material, and provides more accurate electrical parameter guidance for the design and selection of electromagnetic systems such as radar stealth, electromagnetic shielding and radio frequency matching.

Description

Technical Field

[0001] This application relates to the fields of radar stealth and electromagnetic technology, and in particular to a method for inverting the electromagnetic parameters of non-uniform absorbing materials based on the bow-shaped test system. Background Technology

[0002] Microwave-absorbing materials can effectively convert the energy of incident electromagnetic waves into heat or other forms of energy, thus solving problems such as electromagnetic radiation pollution and radar stealth, and are widely used in various fields. Microwave-absorbing materials are usually made by doping a matrix with an absorbing agent, or designed as porous subwavelength structures. Due to limitations in dopant distribution or manufacturing processes, microwave-absorbing materials are often non-uniform. However, accurately measuring the electromagnetic parameters of non-uniform microwave-absorbing materials is a prerequisite for the fine design and optimization of microwave absorbers. Therefore, how to accurately measure the electromagnetic parameters of these materials remains a technical challenge in this field.

[0003] The electromagnetic parameters of non-uniform absorbing materials cannot be directly measured and usually require indirect methods, such as establishing a relationship between scattering parameters and electromagnetic parameters for calculation. Currently common testing methods, such as the transmission-reflection method, typically use waveguides or coaxial lines for measurement, covering a wide frequency range, and the testing methods are relatively mature. However, because the sample needs to be cut into small pieces or rings during measurement, and the processing accuracy directly affects the test results, especially for non-uniform absorbing materials, the special structure and processing difficulty of the material severely affect the measurement accuracy. For soft, deformable absorbing materials (such as foamed materials), when performing millimeter-level cutting, the tolerances of sample size and shape may not meet the standard requirements, thus affecting the accuracy of the test results. Harder materials (such as shielding cement) are not only difficult to process, but also can damage the fixtures during testing. Furthermore, the inhomogeneity of the material's microstructure and dopant distribution can also lead to differences in test results at different locations, further reducing the reliability of the measurement.

[0004] In the inversion of electromagnetic parameters, existing techniques generally rely on traditional inversion algorithms, such as the Nicolson-Ross-Weir (NRW) method. This method is widely used in the calculation of electromagnetic parameters, offering fast solution speed and broad applicability. However, due to the effects of phase ambiguity and thickness resonance, the NRW method suffers from certain multivaluedness issues, which poses a challenge to the accurate inversion of electromagnetic parameters in non-homogeneous materials. Summary of the Invention

[0005] This application provides a method for inverting the electromagnetic parameters of non-uniform absorbing materials based on the bow-shaped method testing system, which can be used to solve the technical problem of the challenge of accurately inverting the electromagnetic parameters of non-uniform materials.

[0006] This application provides a method for inverting the electromagnetic parameters of non-uniform absorbing materials based on a bow-shaped method testing system. The method includes the following steps:

[0007] Step 1: Determine the derivation form of electromagnetic parameters through reflectivity;

[0008] Step 2: Conduct reflectivity testing using the bow-shaped frame system;

[0009] Step 3: Invert the electromagnetic parameters of the non-uniform absorbing material.

[0010] Further, step 1, determining the derivation form of electromagnetic parameters through reflectivity, includes:

[0011] Γ pi The theoretical reflectivity is related to the reflection coefficient Γ and the transmission coefficient T of the material under test, and is expressed by the following formula:

[0012]

[0013] Depending on the polarization of the transmitting and receiving antennas, the reflection coefficient Γ and the transmission coefficient T are expressed as:

[0014]

[0015] The letter subscripts VV (Vertical-Vertical Polarization) and HH (Horizontal-Horizontal Polarization) represent the polarization of the transmitting and receiving antennas, namely vertical polarization and horizontal polarization, respectively; L is the thickness of the absorbing material under test, γ is the propagation constant, β is the phase coefficient, ω is the angular frequency, c is the speed of light, θ is the angle between the test transmitting and receiving antenna and the normal, and ε0 and μ0 are the absolute electromagnetic parameters in vacuum;

[0016] ε r μ r Let be the electromagnetic parameters, representing the complex permittivity and complex permeability respectively, divided into real and imaginary parts, and characterized by the following equation:

[0017]

[0018] Where, ε' r ε” represents the real part of the complex permittivity. r μ' is the imaginary part of the complex permittivity. r μ” represents the real part of the complex permeability. r is the imaginary part of the complex permeability, and j is the imaginary unit;

[0019] As can be seen from equations (1)-(4), there is a correlation between electromagnetic parameters and reflectivity, which can be solved using numerical methods.

[0020] Further, step 2 involves conducting a reflectivity test using a bow-shaped frame system; this includes:

[0021] First, place the metal calibration plate on the platform and test its reflectivity;

[0022] Then, the absorbing material to be tested is placed on a metal calibration plate, and the reflectivity of the absorbing material with the backing metal plate is tested.

[0023] The difference between the reflectivity of the calibration plate and the reflectivity of the absorbing material of the backing metal plate is the required reflectivity Γ. pi ;

[0024] During the test, the test data was time-domain gated to eliminate the influence of background noise; the thickness L of the absorbing material was measured by vernier calipers; and the oblique incidence angle θ was obtained by a high-precision tilt meter on the transceiver antenna.

[0025] Further, step 3 involves inverting the electromagnetic parameters of the non-uniform absorbing material, including:

[0026] When the thickness of the absorbing material under test and the incident angle of the test are determined, the reflectivity Γ pi Only related to the electromagnetic parameter, ε r μ r Relatedly, in equation (1), by differentiating the real and imaginary parts of the electromagnetic parameters respectively, we obtain:

[0027]

[0028] Equation (5) can be simplified as follows:

[0029] JΔX=ΔY (6)

[0030] Where J is the Jacobian matrix, and ΔX and ΔY are respectively represented as:

[0031]

[0032] However, the iterative process is not stable, therefore, equation (7) is modified as follows:

[0033]

[0034] In the above formula, n represents the number of iterations, Γ pmi It is the reflectivity of the absorbing material measured in the i-th test, which remains constant throughout the iteration process;

[0035] From equations (5)-(8), we get:

[0036] X n+1 =X n -J -1 (X n )ΔY(Xn (9)

[0037] The iterative method is the Newton-Raphson iterative algorithm for the nonlinear equation system, and the electromagnetic parameters are obtained from equation (9).

[0038] Furthermore, to satisfy the Jacobian matrix convergence condition, i.e., the matrix condition number ≤ 10, reflectance amplitude data of vertical and horizontal polarization are used instead of single-polarization data.

[0039] Furthermore, in step 2, to satisfy the Jacobian matrix convergence condition, i.e., the matrix condition number ≤ 10, when measuring reflectance, it is required that the test angle θ in a certain polarization direction in the i-th and i+1-th tests be the same. i or θ i+1 Satisfying θ i ,θ i+1 ≥30°, and the difference between the two test angles satisfies |θ i -θ i+1 |≥10°.

[0040] Compared with existing technologies, the significant advantages of this invention are: 1. It adopts the bow-shaped method testing system, which is a non-destructive and non-contact measurement throughout the testing process, and has a wide testing bandwidth (2-40GHz); 2. The bow-shaped method testing system is a mature testing method, and there is no need to rebuild the testing system; 3. In the inversion algorithm, only the amplitude information of reflectivity is used to eliminate the multi-value influence caused by phase ambiguity; 4. In the inversion algorithm, only the amplitude information of dual-polarized multi-angle reflectivity is used, and the electromagnetic parameters can be obtained by testing only one piece of the device under test, which is low cost. Attached Figure Description

[0041] Figure 1 This is a schematic diagram of the bow-shaped testing system mentioned in this invention;

[0042] Figure 2 The reflectivity amplitude information of a certain absorbing material was measured using the bow-shaped method testing system mentioned in this invention.

[0043] Figure 3 The electromagnetic parameters (complex permittivity) are extracted by the inversion algorithm mentioned in this invention. Detailed Implementation

[0044] To make the objectives, technical solutions, and advantages of this application clearer, the embodiments of this application will be described in further detail below with reference to the accompanying drawings.

[0045] The embodiments of this application will now be described in conjunction with the accompanying drawings.

[0046] The main steps of this method include reflectivity testing and an inversion algorithm. In the testing system, destructive testing methods such as the coaxial method and waveguide method are abandoned, and a bow-shaped testing system is adopted to achieve non-destructive, non-contact, and wide-bandwidth measurement. In the inversion algorithm, dual-polarized, oblique-incidence reflectivity data is used, employing a reflectivity amplitude-only inversion method to eliminate the multiple solutions problem caused by phase ambiguity. The purpose of this method is to provide a non-contact, non-destructive, and algorithmically stable method for measuring and inverting the electromagnetic parameters of non-uniform absorbing materials.

[0047] Example 1: A method for inverting the electromagnetic parameters of non-uniform absorbing materials based on the bow-shaped method testing system, mainly including the following steps:

[0048] Step 1: Derivation of electromagnetic parameters from reflectivity amplitude information;

[0049] Γ pi The theoretical reflectivity, which is related to the reflection coefficient Γ and the transmission coefficient T of the material under test, is expressed by the following formula:

[0050]

[0051] Depending on the polarization of the transmitting and receiving antennas, the reflection coefficient Γ and the transmission coefficient T are expressed as:

[0052]

[0053] In the formula, the subscripts VV (Vertical-Vertical Polarization) and HH (Horizontal-Horizontal Polarization) appearing in the letters represent the polarization mode of the transmitting and receiving antennas, which are vertical polarization and horizontal polarization, respectively; L is the thickness of the absorbing material under test, γ is the propagation constant, β is the phase coefficient, ω is the angular frequency, c is the speed of light, θ is the angle between the test transmitting and receiving antenna and the normal, and ε0 and μ0 are the absolute electromagnetic parameters in vacuum;

[0054] ε r μ r For electromagnetic parameters, let represent the complex permittivity and complex permeability respectively, which are divided into real and imaginary parts, and are characterized by equation (4).

[0055]

[0056] Where, ε' r ε” represents the real part of the complex permittivity. r μ' is the imaginary part of the complex permittivity. r μ” represents the real part of the complex permeability. r is the imaginary part of the complex permeability, and j is the imaginary unit;

[0057] As can be seen from the above formula, there is a mathematical relationship between electromagnetic parameters and reflectivity, which can be solved using numerical methods.

[0058] Step 2: Test reflectivity using the bow-shaped frame system.

[0059] Reflectivity Γ pi The reflectivity was obtained through a bow-shaped frame system. First, a metal calibration plate was placed on the stage, and its reflectivity was measured. Then, the absorbing material to be tested was placed on the metal calibration plate, and the reflectivity of the absorbing material against the backing metal plate was measured. The difference between the two reflectivities is the desired reflectivity Γ. pi During the test, the main control computer automatically performs time-domain gating on the test data to eliminate the influence of background noise. The thickness L of the absorbing material can be measured with vernier calipers. The oblique incidence angle θ is obtained from a high-precision tilt meter on the transceiver antenna.

[0060] It is important to note that while the absorbing material under test in this model is theoretically infinitely large, in practical engineering, the absorbing material cannot be an infinitely large medium. Therefore, depending on the test frequency band, the dimensions of the absorbing material under test should satisfy the following requirements:

[0061] (1) 500mm×500mm, dimensional tolerance is ±0.2mm, applicable frequency range is 1GHz~8GHz;

[0062] (2) 300mm×300mm, dimensional tolerance is ±0.1mm, applicable frequency range is 2GHz~18GHz;

[0063] (3) 180mm×180mm, dimensional tolerance is ±0.05mm, applicable frequency range is 6GHz~40GHz;

[0064] Step 3: Invert the electromagnetic parameters of the non-uniform absorbing material:

[0065] When the thickness of the absorbing material under test and the incident angle of the test are determined, the reflectivity Γ pi Only related to the electromagnetic parameter, ε r μ r Relatedly, in equation (1), by differentiating the real and imaginary parts of the electromagnetic parameters respectively, we obtain:

[0066]

[0067] Equation (5) can be simplified as follows:

[0068] JΔX=ΔY (6)

[0069] Where J is the Jacobian matrix, and ΔX and ΔY are respectively represented as:

[0070]

[0071] However, the iterative process is not stable, therefore, equation (7) is modified as follows:

[0072]

[0073] In the above formula, n represents the number of iterations, Γ pmi It is the reflectivity of the absorbing material measured in the i-th test, which remains constant throughout the iteration process;

[0074] The algorithm is the Newton-Raphson iterative algorithm for nonlinear equations, and the electromagnetic parameters can be obtained from equation (7).

[0075] Therefore, in the above embodiments, the testing and inversion methods used are non-contact and non-destructive compared to previous calculation methods. The electromagnetic parameters obtained by the inversion algorithm do not need to consider multiple phase solutions, and only require testing a single piece of absorbing material to obtain the electromagnetic parameters, resulting in lower costs. Therefore, the testing and inversion method of this invention has good prospects for industrial application and research value.

Claims

1. A method for inverting the electromagnetic parameters of non-uniform absorbing materials based on a bow-shaped testing system, characterized in that, The method includes the following steps: Step 1: Determine the derivation form of electromagnetic parameters through reflectivity; Step 2: Conduct reflectivity testing using the bow-shaped frame system; Step 3: Invert the electromagnetic parameters of the non-uniform absorbing material; Step 1: Determine the derivation form of electromagnetic parameters through reflectivity; include: Γ pi The theoretical reflectivity is related to the reflection coefficient Γ and the transmission coefficient T of the material under test, and is expressed by the following formula: Depending on the polarization of the transmitting and receiving antennas, the reflection coefficient Γ and the transmission coefficient T are expressed as: The letter subscripts VV, Vertical-Vertical Polarization, and HH, Horizontal-Horizontal Polarization represent the polarization of the transmitting and receiving antennas, namely vertical polarization and horizontal polarization, respectively; L is the thickness of the absorbing material under test, γ is the propagation constant, β is the phase coefficient, ω is the angular frequency, c is the speed of light, θ is the angle between the test transmitting and receiving antenna and the normal, and ε0 and μ0 are the absolute electromagnetic parameters in vacuum; ε r μ r Let be the electromagnetic parameters, representing the complex permittivity and complex permeability respectively, divided into real and imaginary parts, and characterized by the following equation: Where, ε′ r ε″ is the real part of the complex permittivity. r μ′ is the imaginary part of the complex permittivity. r μ″ is the real part of the complex permeability. r is the imaginary part of the complex permeability, and j is the imaginary unit; As can be seen from equations (1)-(4), there is a correlation between electromagnetic parameters and reflectivity, which can be solved using numerical methods. Step 3, perform the inversion of the electromagnetic parameters of the non-uniform absorbing material, including: When the thickness of the absorbing material under test and the incident angle of the test are determined, the reflectivity Γ pi Only related to the electromagnetic parameter, ε r μ r Relatedly, in equation (1), by differentiating the real and imaginary parts of the electromagnetic parameters respectively, we obtain: Equation (5) can be simplified as follows: JΔX=ΔY (6) Where J is the Jacobian matrix, and ΔX and ΔY are respectively represented as: However, the iterative process is not stable, therefore, equation (7) is modified as follows: In the above formula, n represents the number of iterations, Γ pmi It is the reflectivity of the absorbing material measured in the i-th test, which remains constant throughout the iteration process; From equations (5)-(8), we get: X n+1 =X n -J -1 (X n )ΔY(X n ) (9) The iterative method is the Newton-Raphson iterative algorithm for the nonlinear equation system, and the electromagnetic parameters are obtained from equation (9).

2. The method for inverting electromagnetic parameters of non-uniform absorbing materials based on the bow-shaped method testing system according to claim 1, characterized in that, Step 2, conduct reflectivity testing using the bow-shaped frame system; including: First, place the metal calibration plate on the platform and test its reflectivity; Then, the absorbing material to be tested is placed on a metal calibration plate, and the reflectivity of the absorbing material with the backing metal plate is tested. The difference between the reflectivity of the calibration plate and the reflectivity of the absorbing material of the backing metal plate is the required reflectivity Γ. pi ; During the test, the test data was time-domain gated to eliminate the influence of background noise; the thickness L of the absorbing material was measured by vernier calipers; and the oblique incidence angle θ was obtained by a high-precision tilt meter on the transceiver antenna.

3. The method for inverting electromagnetic parameters of non-uniform absorbing materials based on the bow-shaped method testing system according to claim 1, characterized in that, To satisfy the Jacobian matrix convergence condition, i.e., the matrix condition number ≤ 10, reflectance amplitude data of vertical and horizontal polarization are used instead of single-polarization data.

4. The method for inverting electromagnetic parameters of non-uniform absorbing materials based on the bow-shaped method testing system according to claim 1, characterized in that, In step 2, to satisfy the Jacobian matrix convergence condition (i.e., the condition number ≤ 10), when measuring reflectance, the test angle θ in a certain polarization direction is required to be constant between the i-th and (i+1)-th tests. i or θ i+1 Satisfying θ i ,θ i+1 ≥30°, and the difference between the two test angles satisfies |θ i -θ i+1 |≥10°.

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