Nothing Special   »   [go: up one dir, main page]

CN112462153B - Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate - Google Patents

Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate Download PDF

Info

Publication number
CN112462153B
CN112462153B CN202011293273.1A CN202011293273A CN112462153B CN 112462153 B CN112462153 B CN 112462153B CN 202011293273 A CN202011293273 A CN 202011293273A CN 112462153 B CN112462153 B CN 112462153B
Authority
CN
China
Prior art keywords
antenna
dielectric plate
model
sampling point
dielectric
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Active
Application number
CN202011293273.1A
Other languages
Chinese (zh)
Other versions
CN112462153A (en
Inventor
赵勋旺
陆小文
林中朝
张玉
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN202011293273.1A priority Critical patent/CN112462153B/en
Publication of CN112462153A publication Critical patent/CN112462153A/en
Application granted granted Critical
Publication of CN112462153B publication Critical patent/CN112462153B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01R—MEASURING ELECTRIC VARIABLES; MEASURING MAGNETIC VARIABLES
    • G01R29/00—Arrangements for measuring or indicating electric quantities not covered by groups G01R19/00 - G01R27/00
    • G01R29/08—Measuring electromagnetic field characteristics
    • G01R29/10—Radiation diagrams of antennas

Landscapes

  • Physics & Mathematics (AREA)
  • Electromagnetism (AREA)
  • General Physics & Mathematics (AREA)
  • Aerials With Secondary Devices (AREA)

Abstract

The invention discloses a Fresnel coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab, which comprises the following steps of: (1) mesh subdivision is carried out on the antenna model in the dielectric plate; (2) calculating the mirror image position of the antenna model in the dielectric plate; (3) calculating an electric field generated by the surface current of the antenna model in the dielectric plate; (4) calculating a mirror current; (5) calculating a Fresnel coefficient; (6) calculating an electric field generated by the mirror current; (7) establishing a surface electric field integral equation of an antenna model in a dielectric plate; (8) solving the integral equation of the surface electric field by a moment method; (9) electromagnetic radiation characteristics of the antenna in the dielectric plate are estimated. The method and the device describe the influence of the dielectric plate on the internal antenna by utilizing the Fresnel coefficient, realize the estimation of the radiation characteristic of the antenna in the dielectric plate, provide guidance for the subsequent antenna design and accelerate the design process.

Description

基于菲涅尔系数的介质板内天线辐射特性估计方法Estimation Method of Radiation Characteristics of Antenna in Dielectric Panel Based on Fresnel Coefficient

技术领域technical field

本发明属于通信技术领域，更进一步涉及天线技术领域中的一种基于菲涅尔系数的介质板内天线辐射特性估计方法。本发明可以分析介质板内天线的辐射特性，加快天线设计进程。The invention belongs to the field of communication technology, and further relates to a method for estimating radiation characteristics of an antenna in a dielectric plate based on the Fresnel coefficient in the field of antenna technology. The invention can analyze the radiation characteristic of the antenna in the dielectric plate and speed up the design process of the antenna.

背景技术Background technique

在天线技术领域中，为了保证天线的性能不受外界环境的干扰，通常用天线罩、介质填充等方式来保护天线。天线嵌在介质板内亦是一种常见的方式，如汽车玻璃内的天线。但是这些保护天线的装置也引入了新的问题：外加的装置会对天线的辐射特性产生影响。用矩量法可以分析介质板对天线的辐射特性的影响。In the field of antenna technology, in order to ensure that the performance of the antenna is not disturbed by the external environment, the antenna is usually protected by means of a radome, a dielectric filling, or the like. It is also common for antennas to be embedded in dielectric plates, such as those in automotive glass. But these devices to protect the antenna also introduce a new problem: the additional device will affect the radiation characteristics of the antenna. The influence of the dielectric plate on the radiation characteristics of the antenna can be analyzed by the method of moments.

Faik G.Bogdano等人在其发表的论文“Validation of Hybrid MoM Scheme forComposite Geometries with Layered Structures”(International Seminar/Workshopon Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory(DIPED)，会议论文2016[D])中提出一种基于准静电场分析修正格林函数的电磁估计方法。该方法的实现步骤如下：(1)将天线的表面电流以介质板上下表面为对称面做镜像，并通过准静电场分析计算镜像电流的电流系数。(2)以天线和镜像的电流修正格林函数来构建矩量法的矩阵方程。(3)求解方程后得到天线表面电流，再分析天线的辐射特性。该方法实现了介质板内的天线辐射特性的分析。但是，该方法仍然存在的不足之处是：由于在计算镜像天线的电流系数时，采用的是准静电场分析，用静电场的镜像系数来修正镜像天线的表面电流系数。然而，当介质板的介电常数和介质板外的介电常数相差较小，甚至介质板的介电常数小于介质板外的介电常数时，准静电场分析的精度会下降，进而影响天线辐射特性的分析精度。In their paper "Validation of Hybrid MoM Scheme for Composite Geometries with Layered Structures" by Faik G. Bogdano et al. (International Seminar/Workshopon Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), Conference Paper 2016[D]) An electromagnetic estimation method based on quasi-electrostatic field analysis and modified Green's function is proposed. The implementation steps of the method are as follows: (1) The surface current of the antenna is mirrored with the upper and lower surfaces of the dielectric plate as the symmetry plane, and the current coefficient of the mirrored current is calculated by quasi-electrostatic field analysis. (2) The matrix equation of the method of moments is constructed by correcting the Green's function of the current of the antenna and the mirror. (3) After solving the equation, the surface current of the antenna is obtained, and then the radiation characteristics of the antenna are analyzed. This method realizes the analysis of the radiation characteristics of the antenna in the dielectric plate. However, this method still has the disadvantage that: when calculating the current coefficient of the mirror antenna, the quasi-electrostatic field analysis is used, and the mirror coefficient of the electrostatic field is used to correct the surface current coefficient of the mirror antenna. However, when the difference between the dielectric constant of the dielectric plate and the dielectric constant outside the dielectric plate is small, or even when the dielectric constant of the dielectric plate is smaller than the dielectric constant outside the dielectric plate, the accuracy of the quasi-electrostatic field analysis will decrease, which will affect the antenna. Analytical accuracy of radiation characteristics.

发明内容SUMMARY OF THE INVENTION

本发明的目的在于针对上述现有技术的不足，提出一种基于菲涅尔系数的介质板内天线辐射特性估计方法，解决了介质板的介电常数和介质板外的介电常数相差较小，甚至介质板的介电常数小于介质板外的介电常数时，用准静电场分析估计介质板内天线电磁场辐射特性不准的问题。The purpose of the present invention is to propose a method for estimating the radiation characteristics of an antenna in a dielectric plate based on the Fresnel coefficient, aiming at the shortcomings of the above-mentioned prior art, which solves the problem that the difference between the dielectric constant of the dielectric plate and the dielectric constant outside the dielectric plate is small. , even when the dielectric constant of the dielectric plate is smaller than the dielectric constant outside the dielectric plate, the quasi-electrostatic field analysis is used to estimate the problem of inaccurate radiation characteristics of the antenna electromagnetic field in the dielectric plate.

本发明实现上述目的的思路是，利用菲涅尔系数计算介质板内天线在介质板中产生的电场，构建介质板内天线的表面电场积分方程，由方程得到介质板内天线的表面电流，利用介质板内天线的表面电流来估计介质板内天线的辐射特性。The idea of the present invention to achieve the above object is to use the Fresnel coefficient to calculate the electric field generated by the antenna in the dielectric plate in the dielectric plate, to construct the integral equation of the surface electric field of the antenna in the dielectric plate, to obtain the surface current of the antenna in the dielectric plate from the equation, and to use The surface current of the antenna in the dielectric plate is used to estimate the radiation characteristics of the antenna in the dielectric plate.

本发明的具体步骤如下：The concrete steps of the present invention are as follows:

(1)对介质板内天线模型进行网格剖分：(1) Mesh the antenna model in the dielectric plate:

在[λ/12,λ/8]波长的范围内，将介质板内天线模型剖分成多个三角形网格，根据积分精度的需要设置采样点个数，利用高斯数值积分公式，计算每个三角形网格对应的每个三角形网格高斯采样点位置；Within the wavelength range of [λ/12,λ/8], divide the antenna model in the dielectric plate into multiple triangular meshes, set the number of sampling points according to the integration accuracy, and use the Gaussian numerical integration formula to calculate each triangle The position of each triangle grid Gaussian sampling point corresponding to the grid;

(2)计算介质板内天线模型的镜像位置：(2) Calculate the mirror position of the antenna model in the dielectric plate:

(2a)利用1次镜像公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的第1次镜像；(2a) Calculate the first mirror image of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate by using the first-order mirror formula;

(2b)利用2次镜像公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的第2次镜像；(2b) Calculate the second mirror image of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate by using the 2nd mirror image formula;

(2c)利用m次镜像公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的第m次镜像，m表示大于2且小于20的正整数；(2c) Using the m-th mirror formula, calculate the m-th mirror of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate, where m represents a positive integer greater than 2 and less than 20;

(3)利用求场公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点电流产生的电场：(3) Using the formula for finding the field, calculate the electric field generated by the current at each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate:

(4)利用镜像电流公式，计算介质板内天线模型中每个三角形网格中每个高斯采样点电流的每次镜像电流；(4) Using the mirror current formula, calculate each mirror current of the current of each Gaussian sampling point in each triangular mesh in the antenna model in the dielectric plate;

(5)利用菲涅尔公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的每次镜像后的菲涅尔系数：(5) Using the Fresnel formula, calculate the Fresnel coefficient after each mirror image of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate:

(6)利用下式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的每次镜像电流产生的电场：(6) Using the following formula, calculate the electric field generated by each mirror current of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate:

Figure BDA0002784596110000021
Figure BDA0002784596110000021

Figure BDA0002784596110000022
Figure BDA0002784596110000022

其中，

Figure BDA0002784596110000023
表示介质板内天线模型上第i个三角形网格中第j个高斯采样点的第p次镜像电流在第k个三角形网格上第l个高斯采样点产生的电场，p表示镜像次数的序号，p＝1,2,.....,m，η表示介质板模型的波阻抗，
Figure BDA0002784596110000031
分别表示第i个三角形网格中第j个高斯采样点的第p次镜像与第k个三角形网格上第l个高斯采样点之间的菲涅尔垂直入射面的反射系数、菲涅尔平行入射面的反射系数，L(·)表示电场积分算子，
Figure BDA0002784596110000032
表示第i个三角形网格中第j个高斯采样点的第p次镜像电流；in,
Figure BDA0002784596110000023
Represents the electric field generated by the p-th mirror current of the j-th Gaussian sampling point in the i-th triangular mesh on the dielectric plate antenna model at the l-th Gaussian sampling point on the k-th triangular mesh, p represents the number of mirroring times , p=1,2,.....,m, η represents the wave impedance of the dielectric plate model,
Figure BDA0002784596110000031
Respectively represent the reflection coefficient of the Fresnel vertical incidence surface between the p-th mirror image of the j-th Gaussian sampling point in the ith triangular mesh and the l-th Gaussian sampling point on the k-th triangle mesh, Fresnel The reflection coefficient of the parallel incident plane, L( ) represents the electric field integral operator,
Figure BDA0002784596110000032
represents the p-th mirror current of the j-th Gaussian sampling point in the i-th triangular mesh;

(7)建立介质板内天线模型的表面电场积分方程：(7) Establish the surface electric field integral equation of the antenna model in the dielectric plate:

根据介质板天线模型的边界条件，建立介质板内天线模型上每个三角形网格中每个高斯采样点处的表面电场积分方程；According to the boundary conditions of the dielectric plate antenna model, the integral equation of the surface electric field at each Gaussian sampling point in each triangular mesh on the dielectric plate antenna model is established;

(8)用矩量法解表面电场积分方程：(8) Solve the integral equation of the surface electric field by the method of moments:

用矩量法解介质板内天线的表面电场积分方程，得到介质板内天线模型的表面电流；Solve the integral equation of the surface electric field of the antenna in the dielectric plate by the method of moments, and obtain the surface current of the antenna model in the dielectric plate;

(9)估计介质板内天线的电磁辐射特性：(9) Estimate the electromagnetic radiation characteristics of the antenna in the dielectric plate:

由天线表面电流求解天线辐射问题的相关参数，估计介质板内天线的电磁辐射特性。The relevant parameters of the antenna radiation problem are solved by the antenna surface current, and the electromagnetic radiation characteristics of the antenna in the dielectric plate are estimated.

与现有技术相比，本发明具有以下优点：Compared with the prior art, the present invention has the following advantages:

由于本发明利用菲涅尔系数计算介质板内天线在介质板中产生的电场，克服了在介质板的介电常数和介质板外的介电常数相差较小，甚至介质板的介电常数小于介质板外的介电常数时，准静电场分析描述介质板内天线辐射特性不准确的问题，使得本发明能更准确的描述电磁波在介质板中的传播规律，更精确的估计介质板内天线的电磁辐射特性。Since the invention uses the Fresnel coefficient to calculate the electric field generated by the antenna inside the dielectric plate in the dielectric plate, it overcomes the fact that the dielectric constant of the dielectric plate and the dielectric constant outside the dielectric plate have a small difference, even if the dielectric constant of the dielectric plate is less than When the dielectric constant outside the dielectric plate, the quasi-electrostatic field analysis describes the problem of inaccurate radiation characteristics of the antenna in the dielectric plate, so that the present invention can more accurately describe the propagation law of electromagnetic waves in the dielectric plate, and more accurately estimate the antenna in the dielectric plate. electromagnetic radiation characteristics.

附图说明Description of drawings

图1为本发明的流程图；Fig. 1 is the flow chart of the present invention;

图2为介质板内天线上一点处电流和该电流的部分镜像示意图；Figure 2 is a schematic diagram of the current at a point on the antenna in the dielectric plate and a partial mirror image of the current;

图3为本发明仿真实验中介质板内天线模型的示意图；3 is a schematic diagram of an antenna model in a dielectric plate in a simulation experiment of the present invention;

图4为本发明仿真实验得到的介质板内天线阻抗对比曲线图：其中，图4(a)为本发明仿真实验得到的介质板内天线阻抗实部对比曲线图；图4(b)为本发明仿真实验得到的介质板内天线阻抗虚部对比曲线图。Fig. 4 is a graph showing the comparison of the impedance of the antenna in the dielectric plate obtained by the simulation experiment of the present invention: wherein, Fig. 4(a) is a graph showing the comparison of the real part of the impedance of the antenna in the dielectric plate obtained by the simulation experiment of the present invention; The comparison curve of the imaginary part of the antenna impedance in the dielectric plate obtained by the simulation experiment is invented.

具体实施方式Detailed ways

下面结合附图，对本发明作进一步的详细描述。The present invention will be further described in detail below with reference to the accompanying drawings.

参照附图1，对本发明的具体实施步骤作进一步的详细描述。Referring to FIG. 1 , the specific implementation steps of the present invention will be further described in detail.

步骤1，对介质板内天线模型进行网格剖分。Step 1, meshing the antenna model in the dielectric plate.

在[λ/12,λ/8]波长的范围内，将介质板内天线模型剖分成多个三角形网格，根据积分精度的需要设置采样点个数，利用高斯数值积分公式，计算每个三角形网格对应的每个三角形网格高斯采样点位置；Within the wavelength range of [λ/12,λ/8], divide the antenna model in the dielectric plate into multiple triangular meshes, set the number of sampling points according to the integration accuracy, and use the Gaussian numerical integration formula to calculate each triangle The position of each triangle grid Gaussian sampling point corresponding to the grid;

步骤2，计算介质板内天线模型的镜像位置。Step 2: Calculate the mirror position of the antenna model in the dielectric plate.

利用下述1次镜像公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的第1次镜像：Using the following first-order mirror formula, calculate the first-order mirror image of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate:

Figure BDA0002784596110000041
Figure BDA0002784596110000041

其中，

Figure BDA0002784596110000042
表示介质板内天线模型上第i个三角形网格中第j个高斯采样点的第1次镜像，ri,j表示介质板内天线模型上第i个三角形网格中第j个高斯采样点，di,j表示点ri,j到介质板模型上表面的垂直距离，
Figure BDA00027845961100000412
表示介质板模型上表面的单位法向。in,
Figure BDA0002784596110000042
Represents the first mirror image of the j-th Gaussian sampling point in the i-th triangular mesh on the antenna model in the dielectric plate, and ri ,j represents the j-th Gaussian sampling point in the i-th triangular mesh on the antenna model in the dielectric plate , d i,j represents the vertical distance from the point ri ,j to the upper surface of the dielectric plate model,
Figure BDA00027845961100000412
Represents the unit normal of the upper surface of the dielectric plate model.

利用下述2次镜像公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的第2次镜像：Calculate the second mirror image of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate using the following second-order mirror formula:

Figure BDA0002784596110000043
Figure BDA0002784596110000043

其中，

Figure BDA0002784596110000044
表示第i个三角形网格中第j个高斯采样点的第2次镜像，h表示介质板模型的厚度。in,
Figure BDA0002784596110000044
represents the 2nd mirror image of the jth Gaussian sampling point in the ith triangular mesh, and h represents the thickness of the dielectric plate model.

利用下述m次镜像公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的第m次镜像，m表示大于2且小于20的正整数：Use the following m-th mirror formula to calculate the m-th mirror of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate, where m represents a positive integer greater than 2 and less than 20:

Figure BDA0002784596110000045
Figure BDA0002784596110000045

其中，

Figure BDA0002784596110000046
表示介质板内天线模型上第i个三角形网格中第j个高斯采样点的第m次镜像，
Figure BDA0002784596110000047
表示介质板内天线模型上第i个三角形网格中第j个高斯采样点的第m-2次镜像；当m-2为奇数时，
Figure BDA0002784596110000048
表示点
Figure BDA0002784596110000049
到介质板模型下表面的垂直距离，当m-2为偶数时，
Figure BDA00027845961100000410
表示点
Figure BDA00027845961100000411
到介质板模型上表面的垂直距离。in,
Figure BDA0002784596110000046
represents the mth mirror image of the jth Gaussian sampling point in the ith triangular mesh on the antenna model in the dielectric plate,
Figure BDA0002784596110000047
Represents the m-2th mirror image of the jth Gaussian sampling point in the ith triangular mesh on the antenna model in the dielectric plate; when m-2 is an odd number,
Figure BDA0002784596110000048
Representation point
Figure BDA0002784596110000049
The vertical distance to the lower surface of the dielectric plate model, when m-2 is an even number,
Figure BDA00027845961100000410
Representation point
Figure BDA00027845961100000411
The vertical distance to the top surface of the dielectric plate model.

图2为介质板内天线上一点处电流和该电流的部分镜像示意图，其中，方框为介质板的纵向切面，ri,j为介质板内天线模型上第i个三角形网格中第j个高斯采样点，

Figure BDA0002784596110000051
分别为点ri,j的第1、2、3、4次镜像，箭头为每个点及镜像对应的电流。Figure 2 is a schematic diagram of the current at a point on the antenna in the dielectric plate and the partial mirror image of the current, in which the box is the longitudinal section of the dielectric plate, and ri ,j is the jth in the i-th triangular mesh on the antenna model in the dielectric plate. Gaussian sampling points,
Figure BDA0002784596110000051
are the 1st, 2nd, 3rd, and 4th mirror images of points ri ,j , respectively, and the arrows are the currents corresponding to each point and mirror image.

步骤3，利用下述求场公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点电流产生的电场：Step 3: Calculate the electric field generated by the current of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate by using the following formula for finding the field:

Ei,j、k,l＝ηL(Ji,j)E i,j, k,l =ηL(J i,j )

其中，Ei,j、k,l表示介质板内天线模型上第i个三角形网格中第j个高斯采样点电流在第k个三角形网格上第l个高斯采样点产生的电场，Ji,j表示第i个三角形网格中第j个高斯采样点电流。Among them, E i,j, k,l represent the electric field generated by the current of the jth Gaussian sampling point in the ith triangular mesh on the dielectric plate antenna model at the lth Gaussian sampling point on the kth triangular mesh, J i,j represents the current of the jth Gaussian sampling point in the ith triangular mesh.

步骤4，利用下述镜像电流公式，计算介质板内天线模型中每个三角形网格中每个高斯采样点电流的每次镜像电流：Step 4, use the following image current formula to calculate each image current of each Gaussian sampling point current in each triangular mesh in the antenna model in the dielectric plate:

Figure BDA0002784596110000052
Figure BDA0002784596110000052

Figure BDA0002784596110000053
Figure BDA0002784596110000053

其中，

Figure BDA0002784596110000054
表示将电流Ji,j投影到介质板模型上表面外法向得到的电流Ji,j垂直分量。in,
Figure BDA0002784596110000054
represents the vertical component of the current J i,j obtained by projecting the current J i,j to the outer normal of the upper surface of the dielectric plate model.

步骤5，利用下述菲涅尔公式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的每次镜像后的菲涅尔系数：Step 5, using the following Fresnel formula, calculate the Fresnel coefficient after each mirror image of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate:

Figure BDA0002784596110000055
Figure BDA0002784596110000055

Figure BDA0002784596110000056
Figure BDA0002784596110000056

其中，

Figure BDA0002784596110000057
分别表示第i个三角形网格中第j个高斯采样点的第p次镜像与第k个三角形网格上第l个高斯采样点之间的菲涅尔垂直入射面的反射系数、菲涅尔平行入射面的反射系数；εr1表示介质板模型内的相对介电常数，εr2表示介质板模型外自由空间的相对介电常数，sin表示正弦操作，cos表示余弦操作，
Figure BDA0002784596110000058
表示第i个三角形网格中第j个高斯采样点的第p次镜像与第k个三角形网格上第l个高斯采样点连线的单位向量与介质板模型上表面法向之间的夹角。in,
Figure BDA0002784596110000057
Respectively represent the reflection coefficient of the Fresnel vertical incidence surface between the p-th mirror image of the j-th Gaussian sampling point in the ith triangular mesh and the l-th Gaussian sampling point on the k-th triangle mesh, Fresnel The reflection coefficient of the parallel incident surface; ε r1 represents the relative permittivity inside the dielectric plate model, ε r2 represents the relative permittivity of the free space outside the dielectric plate model, sin represents the sine operation, cos represents the cosine operation,
Figure BDA0002784596110000058
Represents the clip between the unit vector of the line connecting the p-th mirror image of the j-th Gaussian sampling point in the i-th triangular mesh and the l-th Gaussian sampling point on the k-th triangular mesh and the normal to the upper surface of the dielectric plate model horn.

步骤6，利用下式，计算介质板内天线模型上每个三角形网格中每个高斯采样点的每次镜像电流产生的电场：Step 6, use the following formula to calculate the electric field generated by each mirror current of each Gaussian sampling point in each triangular mesh on the antenna model in the dielectric plate:

Figure BDA0002784596110000061
Figure BDA0002784596110000061

Figure BDA0002784596110000062
Figure BDA0002784596110000062

其中，

Figure BDA0002784596110000063
表示介质板内天线模型上第i个三角形网格中第j个高斯采样点的第p次镜像电流在第k个三角形网格上第l个高斯采样点产生的电场，p表示镜像次数的序号，p＝1,2,.....,m，η表示介质板模型的波阻抗，
Figure BDA0002784596110000064
分别表示第i个三角形网格中第j个高斯采样点的第p次镜像与第k个三角形网格上第l个高斯采样点之间的菲涅尔垂直入射面的反射系数、菲涅尔平行入射面的反射系数，L(·)表示电场积分算子，
Figure BDA0002784596110000065
表示第i个三角形网格中第j个高斯采样点的第p次镜像电流。in,
Figure BDA0002784596110000063
Represents the electric field generated by the p-th mirror current of the j-th Gaussian sampling point in the i-th triangular mesh on the dielectric plate antenna model at the l-th Gaussian sampling point on the k-th triangular mesh, p represents the number of mirroring times , p=1,2,.....,m, η represents the wave impedance of the dielectric plate model,
Figure BDA0002784596110000064
Respectively represent the reflection coefficient of the Fresnel vertical incidence surface between the p-th mirror image of the j-th Gaussian sampling point in the ith triangular mesh and the l-th Gaussian sampling point on the k-th triangle mesh, Fresnel The reflection coefficient of the parallel incident plane, L( ) represents the electric field integral operator,
Figure BDA0002784596110000065
represents the p-th mirror current of the j-th Gaussian sampling point in the i-th triangular mesh.

步骤7，建立介质板内天线模型的表面电场积分方程。Step 7, establishing the surface electric field integral equation of the antenna model in the dielectric plate.

根据介质板天线模型的边界条件，建立介质板内天线模型上每个三角形网格中每个高斯采样点处的表面电场积分方程如下：According to the boundary conditions of the dielectric plate antenna model, the integral equation of the surface electric field at each Gaussian sampling point in each triangular mesh on the dielectric plate antenna model is established as follows:

Figure BDA0002784596110000066
Figure BDA0002784596110000066

其中，

Figure BDA0002784596110000067
表示介质板内天线模型上第k个三角形网格的外法向，i表示介质板内天线模型剖分的三角形网格的序号，α表示介质板内天线模型剖分的三角形网格的总数，j表示三角形网格上高斯采样点序号，β表示三角形网格上的高斯采样点的总数；
Figure BDA0002784596110000068
表示第k个三角形网格上第l个高斯采样点的外加激励场。in,
Figure BDA0002784596110000067
represents the outer normal of the kth triangular mesh on the antenna model in the dielectric plate, i represents the serial number of the triangular meshes divided by the antenna model in the dielectric plate, α represents the total number of triangular meshes divided by the antenna model in the dielectric plate, j represents the number of Gaussian sampling points on the triangular mesh, and β represents the total number of Gaussian sampling points on the triangular mesh;
Figure BDA0002784596110000068
Represents the applied excitation field at the l-th Gaussian sampling point on the k-th triangular mesh.

步骤8，用矩量法解表面电场积分方程。Step 8: Solve the integral equation of the surface electric field by the method of moments.

用矩量法解介质板内天线的表面电场积分方程，得到介质板内天线模型的表面电流。Solve the integral equation of the surface electric field of the antenna in the dielectric plate by the method of moments, and obtain the surface current of the antenna model in the dielectric plate.

步骤9，估计介质板内天线的电磁辐射特性。Step 9, estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate.

由天线表面电流求解天线辐射问题的相关参数，估计介质板内天线的电磁辐射特性。The relevant parameters of the antenna radiation problem are solved by the antenna surface current, and the electromagnetic radiation characteristics of the antenna in the dielectric plate are estimated.

下面结合仿真实验对本发明的效果做进一步说明。The effect of the present invention will be further described below in conjunction with simulation experiments.

1.仿真条件：1. Simulation conditions:

本发明的仿真实验条件：处理器型号为Intel(R)Core(TM)i5-8250U 1.6GHz CPU、8GB RAM；编程语言为Fortran。The simulation experiment conditions of the present invention: the processor model is Intel(R) Core(TM) i5-8250U 1.6GHz CPU, 8GB RAM; the programming language is Fortran.

2.仿真内容与结果分析：2. Simulation content and result analysis:

本发明仿真实验的模型是由介质板模型和偶极子天线模型组成的介质板内天线模型。该模型如图3所示，图中长方体为介质板模型，长1.2m，宽1m，高0.3m，相对介电常数为2.0。长方体内部的两个相同狭长矩形组成了偶极子天线，两个矩形的连接处为外加激励位置，偶极子天线中心与介质板中心重合，每个矩形长0.5m，宽0.02m。本仿真实验中介质板所在自由空间的相对介电常数为6.0。The model of the simulation experiment of the present invention is an antenna model in a dielectric plate composed of a dielectric plate model and a dipole antenna model. The model is shown in Figure 3, in which the cuboid is a dielectric plate model with a length of 1.2m, a width of 1m, a height of 0.3m, and a relative permittivity of 2.0. The two same narrow and long rectangles inside the cuboid form a dipole antenna. The connection of the two rectangles is the position of the external excitation. The center of the dipole antenna coincides with the center of the dielectric plate. Each rectangle is 0.5m long and 0.02m wide. In this simulation experiment, the relative permittivity of the free space where the dielectric plate is located is 6.0.

本发明的仿真实验是采用本发明方法和现有技术基于准静电场分析修正格林函数的电磁估计方法(参见背景技术中所提到的Faik G.Bogdano在其发表的论文“Validation of Hybrid MoM Scheme for Composite Geometries with LayeredStructures”(International Seminar/Workshop on Direct and Inverse Problems ofElectromagnetic and Acoustic Wave Theory(DIPED)，会议论文2016[D]))分别对介质板内天线模型的进行仿真，计算介质板内天线模型的天线阻抗。其中，偶极子天线的激励电压为1V，扫频范围为100MHz～700MHz，频率间隔为12MHz，得到介质板内偶极子天线阻抗随频率变化的曲线。The simulation experiment of the present invention is based on the method of the present invention and the prior art based on the quasi-electrostatic field analysis to correct the Green's function of electromagnetic estimation method (refer to the paper "Validation of Hybrid MoM Scheme" published by Faik G. Bogdano mentioned in the background art. For Composite Geometries with LayeredStructures” (International Seminar/Workshop on Direct and Inverse Problems of Electromagnetic and Acoustic Wave Theory (DIPED), conference paper 2016[D])) respectively simulate the antenna model in the dielectric plate, and calculate the antenna model in the dielectric plate the antenna impedance. Among them, the excitation voltage of the dipole antenna is 1V, the frequency sweep range is 100MHz-700MHz, and the frequency interval is 12MHz, and the curve of the impedance of the dipole antenna in the dielectric plate changing with frequency is obtained.

为了验证本发明方法和现有技术的仿真效果，用商业软件FEKO的Windscreen电磁仿真方法对上述仿真条件对本仿真实验模型进行仿真，计算介质板内天线的天线阻抗，扫频范围为100MHz～700MHz，频率间隔为12MHz得到介质板内偶极子天线阻抗随频率变化的曲线。In order to verify the simulation effect of the method of the present invention and the prior art, use the Windscreen electromagnetic simulation method of commercial software FEKO to simulate the simulation experiment model for the above simulation conditions, calculate the antenna impedance of the antenna in the dielectric plate, and the sweep frequency range is 100MHz～700MHz, The frequency interval is 12MHz to obtain the curve of the impedance of the dipole antenna in the dielectric plate as a function of frequency.

图4(a)为本发明仿真实验得到的介质板内天线阻抗实部对比曲线图，图4(b)为本发明仿真实验得到的介质板内天线阻抗虚部对比曲线图。图4(a)、图4(b)中横坐标表示频率，单位为MHz，纵坐标表示阻抗，单位为Ohm。图4(a)、图4(b)中以正方形标示的曲线分别表示采用本发明方法仿真得到的天线阻抗的实部和虚部曲线。图4(a)、图4(b)中以圆形标示的曲线分别表示商业软件FEKO仿真得到的天线阻抗实部和虚部曲线；图4(a)、图4(b)中以三角形标示的曲线分别表示采用现有技术仿真得到的天线阻抗实部和虚部曲线。从图4(a)的曲线图中可以看出，在150MHz到180MHz和340MHz到370MHz频率范围，本发明方法仿真结果和商业软件FEKO仿真结果吻合的更好；从图4(b)的曲线图中可以看出，在150MHz到220MHz和320MHz到380MHz频率范围，本发明方法仿真结果和商业软件FEKO仿真结果吻合的更好。由此可以看出，本发明方法的仿真结果精度更高。Fig. 4(a) is a graph showing the comparison of the real part of the antenna impedance in the dielectric plate obtained by the simulation experiment of the present invention, and Fig. 4(b) is a graph showing the comparison of the imaginary part of the antenna impedance in the dielectric plate obtained by the simulation experiment of the present invention. In Fig. 4(a) and Fig. 4(b), the abscissa represents the frequency, and the unit is MHz, and the ordinate represents the impedance, and the unit is Ohm. The curves marked with squares in Fig. 4(a) and Fig. 4(b) respectively represent the real part and imaginary part curves of the antenna impedance simulated by the method of the present invention. The curves marked with circles in Figure 4(a) and Figure 4(b) represent the real and imaginary part curves of the antenna impedance simulated by the commercial software FEKO, respectively; the curves marked with triangles in Figure 4(a) and Figure 4(b) The curves of , respectively represent the real part and imaginary part curves of the antenna impedance obtained by the simulation using the prior art. It can be seen from the graph of Fig. 4(a) that in the frequency ranges of 150MHz to 180MHz and 340MHz to 370MHz, the simulation results of the method of the present invention are in better agreement with the simulation results of the commercial software FEKO; from the graph of Fig. 4(b) It can be seen that in the frequency range of 150MHz to 220MHz and 320MHz to 380MHz, the simulation results of the method of the present invention are in better agreement with the simulation results of the commercial software FEKO. It can be seen from this that the simulation result of the method of the present invention has higher precision.

Claims (8)

1. A Fresnel coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab is characterized in that an electric field generated by the antenna in the dielectric slab is calculated by utilizing the Fresnel coefficient, a surface electric field integral equation of the antenna in the dielectric slab is constructed, surface currents of the antenna in the dielectric slab are obtained by the equation, and the radiation characteristics of the antenna in the dielectric slab are estimated by utilizing the surface currents of the antenna in the dielectric slab; the method comprises the following specific steps:
(1) and (3) carrying out mesh subdivision on the antenna model in the dielectric plate:
within the range of [ lambda/12, lambda/8 ] wavelength, dividing an antenna model in the dielectric slab into a plurality of triangular meshes, setting the number of sampling points according to the requirement of integration precision, and calculating the position of each triangular mesh Gaussian sampling point corresponding to each triangular mesh by using a Gaussian numerical integration formula;
(2) calculating the mirror image position of the antenna model in the dielectric plate:
(2a) calculating the 1 st mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a 1 st mirror image formula;
(2b) calculating the 2 nd time mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a 2-time mirror image formula;
(2c) calculating the mth mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using an m-order mirror image formula, wherein m represents a positive integer which is more than 2 and less than 20;
(3) calculating an electric field generated by the surface current of the antenna model in the dielectric plate:
calculating an electric field generated by each Gaussian sampling point current in each triangular grid on the antenna model in the dielectric plate by using a field solving formula:
(4) calculating each mirror current of each Gaussian sampling point current in each triangular grid in the antenna model in the dielectric plate by using a mirror current formula;
(5) calculating the Fresnel coefficient after each mirror image of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric slab by using a Fresnel formula:
(6) calculating the electric field generated by each mirror current of each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate by using the following formula:
Figure FDA0002784596100000011
Figure FDA0002784596100000021
wherein,
Figure FDA0002784596100000022
an electric field generated by the p-th image-reflecting current of the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab at the ith Gaussian sampling point on the kth triangular grid is represented, p represents the sequence number of image times, p is 1,2, the.
Figure FDA0002784596100000023
Respectively showing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid, L (-) shows an electric field integral operator,
Figure FDA0002784596100000024
representing the p-th image current of the j-th Gaussian sampling point in the ith triangular grid;
(7) establishing a surface electric field integral equation of an antenna model in a dielectric plate:
establishing a surface electric field integral equation at each Gaussian sampling point in each triangular grid on the antenna model in the dielectric plate according to the boundary condition of the dielectric plate antenna model;
(8) solving the integral equation of the surface electric field by a moment method:
solving a surface electric field integral equation of the antenna model in the dielectric plate by a moment method to obtain the surface current of the antenna model in the dielectric plate;
(9) estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate:
and solving related parameters of the antenna radiation problem by the antenna surface current, and estimating the electromagnetic radiation characteristic of the antenna in the dielectric plate.
2. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients as defined in claim 1, wherein the 1-time mirror image formula in step (2a) is as follows:
Figure FDA0002784596100000025
wherein,
Figure FDA0002784596100000026
representing the 1 st mirror image of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric platei,jRepresents the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate, di,jRepresents a point ri,jThe vertical distance to the upper surface of the dielectric slab model,
Figure FDA0002784596100000027
which represents the unit normal direction of the upper surface of the dielectric slab model.
3. The fresnel-coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab according to claim 2, wherein the 2-time mirror equation in step (2b) is as follows:
Figure FDA0002784596100000031
wherein,
Figure FDA0002784596100000032
and (4) representing the 2 nd mirror image of the jth Gaussian sampling point in the ith triangular grid, and h represents the thickness of the dielectric slab model.
4. The fresnel-coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab according to claim 2, wherein the m-order mirror image formula in step (2c) is as follows:
Figure FDA0002784596100000033
wherein,
Figure FDA0002784596100000034
representing the m-th mirror image of the j-th Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab,
Figure FDA0002784596100000035
representing the m-2 th mirror image of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric slab; when m-2 is an odd number,
Figure FDA0002784596100000036
indicating points
Figure FDA0002784596100000037
When the vertical distance from the lower surface of the dielectric slab model is m-2 is an even number,
Figure FDA0002784596100000038
indicating points
Figure FDA0002784596100000039
The vertical distance to the upper surface of the dielectric slab model.
5. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients as defined in claim 1, wherein the field-finding formula in step (3) is as follows:
Ei,j、k,l＝ηL(Ji,j)
wherein E isi,j、k,lThe electric field generated by the current of the jth Gaussian sampling point in the ith triangular grid on the antenna model in the dielectric plate at the ith Gaussian sampling point on the kth triangular grid is represented, Ji,jRepresenting the current at the jth gaussian sample point in the ith triangular grid.
6. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients as defined in claim 5, wherein the mirror current formula in step (4) is as follows:
Figure FDA00027845961000000310
Figure FDA00027845961000000311
wherein,
Figure FDA00027845961000000312
represents the current Ji,jCurrent J obtained by projecting to the outside of the upper surface of the dielectric slab model in the normal directioni,jThe vertical component.
7. The method for estimating radiation characteristics of an antenna in a dielectric slab based on fresnel coefficients according to claim 1, wherein the fresnel formula in step (5) is as follows:
Figure FDA0002784596100000041
Figure FDA0002784596100000042
wherein,
Figure FDA0002784596100000043
respectively representing the reflection coefficient of a Fresnel vertical incidence surface and the reflection coefficient of a Fresnel parallel incidence surface between the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid; epsilonr1Represents the relative dielectric constant, ε, in a dielectric slab modelr2Representing the relative permittivity of the free space outside the dielectric slab model, sin represents the sine operation, cos represents the cosine operation,
Figure FDA0002784596100000044
and representing the included angle between the unit vector of the connecting line of the p-th mirror image of the jth Gaussian sampling point in the ith triangular grid and the ith Gaussian sampling point on the kth triangular grid and the normal direction of the upper surface of the dielectric slab model.
8. The fresnel-coefficient-based method for estimating radiation characteristics of an antenna in a dielectric slab according to claim 5, wherein the surface electric field integral equation in step (7) is as follows:
Figure FDA0002784596100000045
wherein,
Figure FDA0002784596100000046
the external normal direction of the kth triangular grid on the antenna model in the dielectric plate is represented, i represents the serial number of the triangular grid split by the antenna model in the dielectric plate, alpha represents the total number of the triangular grids split by the antenna model in the dielectric plate, j represents the serial number of Gaussian sampling points on the triangular grid, and beta represents the total number of the Gaussian sampling points on the triangular grid;
Figure FDA0002784596100000047
the applied excitation field of the ith Gaussian sample point on the kth triangular mesh is shown.
CN202011293273.1A 2020-11-18 2020-11-18 Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate Active CN112462153B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202011293273.1A CN112462153B (en) 2020-11-18 2020-11-18 Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202011293273.1A CN112462153B (en) 2020-11-18 2020-11-18 Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate

Publications (2)

Publication Number Publication Date
CN112462153A CN112462153A (en) 2021-03-09
CN112462153B true CN112462153B (en) 2021-07-27

Family

ID=74837761

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202011293273.1A Active CN112462153B (en) 2020-11-18 2020-11-18 Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate

Country Status (1)

Country Link
CN (1) CN112462153B (en)

Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5972066A (en) * 1982-10-18 1984-04-23 Nec Corp Antenna measuring device
CN104750917A (en) * 2015-03-11 2015-07-01 西安电子科技大学 Determination method for layered medium rough surface electromagnetic scattering coefficients
CN105789875A (en) * 2016-04-13 2016-07-20 西安电子科技大学 Low-profile broadband dual polarized antenna
CN108352612A (en) * 2015-09-11 2018-07-31 Cpg技术有限责任公司 The guiding surface optical waveguide probe of enhancing
CN110750929A (en) * 2019-10-15 2020-02-04 电子科技大学 An Analysis Method of Antenna Radiation and Scattering Characteristics Based on Eigenmode Theory

Patent Citations (5)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
JPS5972066A (en) * 1982-10-18 1984-04-23 Nec Corp Antenna measuring device
CN104750917A (en) * 2015-03-11 2015-07-01 西安电子科技大学 Determination method for layered medium rough surface electromagnetic scattering coefficients
CN108352612A (en) * 2015-09-11 2018-07-31 Cpg技术有限责任公司 The guiding surface optical waveguide probe of enhancing
CN105789875A (en) * 2016-04-13 2016-07-20 西安电子科技大学 Low-profile broadband dual polarized antenna
CN110750929A (en) * 2019-10-15 2020-02-04 电子科技大学 An Analysis Method of Antenna Radiation and Scattering Characteristics Based on Eigenmode Theory

Non-Patent Citations (1)

* Cited by examiner, † Cited by third party
Title
双层手征介质板中电偶极天线的辐射特性;尹文言 等;《电子科学学刊》;19940731;第16卷(第4期);第432-438页 *

Also Published As

Publication number Publication date
CN112462153A (en) 2021-03-09

Similar Documents

Publication Publication Date Title
CN106228971B (en) Based on the broadband sound focusing lens and preparation method thereof for dividing shape acoustic metamaterial
US20070069940A1 (en) Method and arrangement for reducing the radar cross section of integrated antennas
Cai et al. Volume surface integral equation method based on higher order hierarchical vector basis functions for EM scattering and radiation from composite metallic and dielectric structures
CN105786765B (en) A kind of method generating excitation extraneous features basic function quick self-adaptedly
CN103065007B (en) A kind of antenna modeling method based on directional diagram and input impedance test data
CN109766630B (en) Equivalent electromagnetic parameter extraction method of honeycomb wave-absorbing material
CN107305536B (en) Mixed order time domain discontinuous Galois field gold method
CN112462153B (en) Fresnel coefficient-based method for estimating radiation characteristics of antennas in dielectric plate
CN108664746B (en) Frequency selection surface approximate analysis method based on double-line transmission line model
CN110274920A (en) The method of honorable subdivision Shooting and bouncing rays analysis metal medium target transient response
CN112068101B (en) Target scattering separation method based on mode filtering
CN105844019A (en) Ground point selection method based on vehicle ground current distribution regularities
CN110738009B (en) A method for setting the analog charge in the wire in the calculation of the electric field of the transmission line
US12126396B2 (en) Domain decomposition method and system for electromagnetic simulation
Jacobs et al. Validation of a computational electromagnetic model of a boeing 707 aircraft by comparison to scale model measurements
CN109614732A (en) A kind of the electromagnetic compatibility modeling method and device of object
Zhao et al. RCS prediction of polygonal metal plate based on machine learning
CN115659607A (en) Method for determining multilayer wave-transparent structure
CN103474737A (en) Millimeter wave E-plane filter for supporting vector machine to model for diaphragm and diaphragm modeling method
CN113177307A (en) Short-wave ground wave simulation method and system applied to complex terrain
CN117057098B (en) Frequency-selective radome analysis method based on physical optics and equivalent medium model
Wang et al. Edge diffraction in NURBS-UTD method
Zeyde et al. A free-space samples material parameters validation technique
Culhaoglu et al. Modeling and simulation of electromagnetic scattering from electrically large bodies coated with CLS-based metamaterial absorbers
CN118098457A (en) Comprehensive evaluation and analysis method for electromagnetic shielding effectiveness of complex curved micro-nanostructures

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant