Linear array antenna single-plane near-field measurement method based on equivalent source method

Abstract

The application provides a linear array antenna single-section near-field measurement method based on an equivalent source method, and the implementation steps are as follows: obtaining a near-field electric field signal of a linear array antenna at a working frequency point; constructing an equivalent source model; obtaining a correlation coefficient matrix; obtaining an equivalent source base function coefficient vector; and obtaining a linear array antenna single-section near-field measurement result. The equivalent source model constructed by the application is a model comprising M equivalent source points which are linearly arranged along the linear array antenna and whose centers are located at the origin of a planar rectangular coordinate system, the correlation coefficient matrix calculated by the linear equivalent source model of the prior art contains fewer elements, and only vector and matrix calculations are needed in the calculation of the equivalent source base function coefficients, thus avoiding the defect that the prior art uses the planar equivalent source model to cause the need for complex matrix calculation, and effectively improving the measurement efficiency.

Description

Technical Field

[0001] This invention belongs to the field of antenna measurement and relates to a near-field measurement method for linear array antennas. Specifically, it relates to a single-section near-field measurement method for linear array antennas based on the equivalent source method, which can be used for the design, development and maintenance of linear array antennas. Background Technology

[0002] One-dimensional linear antenna arrays have wide applications in base station antenna design, phased array design, and other technical design fields. The research, design, and maintenance of one-dimensional linear array antennas are inseparable from near-field measurement technology. Normally, near-field measurements of array antennas require three-dimensional sampling scanning methods. However, since one-dimensional linear antenna arrays primarily focus on the radiation pattern characteristics of the array dimension's cross-section, a simplified two-dimensional single-section near-field measurement method can be used. This two-dimensional single-section near-field measurement method can be further categorized into spectral expansion methods, equivalent source methods, and multipole expansion algorithms, based on far-field extrapolation techniques. For the equivalent source method, the discrete near-field electric field signal matrix at the center operating frequency of the antenna array under test is typically obtained through sampling. Then, an equivalent source model is constructed, and the correlation coefficient matrix is ​​calculated. The equivalent source basis function coefficient matrix is ​​calculated using the electric field signal matrix and the correlation coefficient matrix. Finally, far-field extrapolation is performed on the equivalent source basis function coefficient vector to obtain the single-section far-field radiation pattern. The efficiency and accuracy of near-field measurements have a crucial impact on antenna design, making research on efficient and accurate near-field measurements extremely important.

[0003] However, current near-field measurement methods based on the equivalent source method employ two-dimensional equivalent source models. The complexity of the equivalent source basis function coefficient matrix and correlation coefficient matrix is ​​related to the complexity of the equivalent source model; the higher the dimension of the equivalent source model, the more complex the corresponding matrices. For example, in his paper "Using Planar Probe Array Near Field Measurement to Obtain Accurate Far Field Antenna Pattern Efficiently" published on page 1109 of the proceedings of the 2019 IEEE International Conference on Computational Electromagnetics (ICCEM), H. Chen disclosed a novel near-field measurement method for determining a two-dimensional single-section of a linear antenna array using the equivalent source method. This method first uses a planar probe to obtain the near-field electric field signal matrix at the operating frequency of the linear array antenna. Then, it constructs a two-dimensional planar equivalent source model and calculates the correlation coefficient matrix. The equivalent source basis function coefficient matrix is ​​then calculated using the electric field signal matrix and the correlation coefficient matrix. Finally, the far-field radiation pattern of the single-section is obtained by far-field extrapolation of the equivalent source basis function coefficient matrix. Compared to traditional measurement methods, this method uses a planar probe to acquire the near-field electric field signal in one go, which simplifies the measurement process and improves efficiency to some extent. However, its shortcomings are that using a two-dimensional planar equivalent source model requires complex matrix calculations, resulting in relatively low measurement efficiency. Summary of the Invention

[0004] The purpose of this invention is to address the shortcomings of the prior art by proposing a single-section near-field measurement method for linear array antennas based on the equivalent source method, which solves the technical problem of low measurement efficiency caused by the complex structure of the equivalent source model in the prior art.

[0005] To achieve the above objectives, the technical solution adopted by the present invention includes the following steps:

[0006] (1) Obtain the near-field electric field signal at the operating frequency of the linear array antenna:

[0007] (1a) The operating frequency of the linear array antenna whose center is located at the origin of the plane rectangular coordinate system and is arranged along the Y direction is f0, the wavelength corresponding to f0 is λ0, and the length of the linear array antenna is d.

[0008] (1b) Perform C near-field samplings on the near-field region of the linear array antenna at frequency point f0 to obtain the discrete electric field signal vector U. C×1 ={U1,U2,...,U c ,...,U C}, where Uc This indicates that the c-th coordinate is (x c ,y c The discrete electric field signal corresponding to the sampling point of ), c∈{1,2,...,C};

[0009] (2) Constructing an equivalent source model:

[0010] Construct an equivalent source model comprising M equivalent source points centered at the origin of a Cartesian coordinate system and linearly arranged along the Y direction. The distance between adjacent equivalent source points is Δλ0, and the coordinates of the m-th equivalent source point are (x'...). m ,y' m ), where Δλ0≥0.001λ0, m∈{1,2,...,M}, Indicates rounding up;

[0011] (3) Obtain the correlation coefficient matrix:

[0012] (3a) Through the coordinates (x) of each sampling point c ,y c ) and the coordinates (x') of each equivalent source point m ,y' m Calculate the distance R from each equivalent source point to each sampling point. c,m ;

[0013] (3b) The distance R from each equivalent source point to each sampling point c,m and related basis functions Λ m Calculate the correlation coefficient A for (x, y). c,m and all correlation coefficients A c,m The combination forms a correlation coefficient matrix A of dimension C×M. C×M The correlation coefficient A c,m The calculation formula is:

[0014]

[0015]

[0016] in Indicated by S m The double integral over the boundary, where e denotes the natural logarithm, Λ m (x,y) represents the m-th associated basis function with independent variable coordinates x and y on the x and y axes, respectively. m Represents Λ m The distribution region of (x,y);

[0017] (4) Obtain the equivalent source basis function coefficient vector:

[0018] The method of moments is employed, and the discrete electric field signal vector U at frequency point f0 is used.C×1 With correlation coefficient matrix A C×M Calculate the equivalent source basis function coefficient vector J M×1 ;

[0019] (5) Obtain near-field measurement results of a single cross-section of the linear array antenna:

[0020] For the equivalent source basis function coefficient vector J M×1 Perform far-field extrapolation to obtain polar coordinates with the following values: The far-field radiation pattern of a single tangent at the center working frequency point of the angular coordinate system.

[0021]

[0022] Among them, J m J represents the equivalent source basis function coefficient vector. M×1 The coefficients of the m-th equivalent source basis function in the equation.

[0023] Compared with the prior art, the present invention has the following advantages:

[0024] The equivalent source model constructed in this invention comprises M equivalent source points centered at the origin of the Cartesian coordinate system and linearly arranged along the linear array antenna. Compared with the correlation coefficient matrix calculated by the linear equivalent source model in the prior art, it contains fewer elements. Furthermore, in the calculation of the equivalent source basis function coefficients, only vector and matrix calculations are required, which avoids the defects of complex matrix calculations caused by the use of the planar equivalent source model in the prior art, and effectively improves the measurement efficiency. Attached Figure Description

[0025] Figure 1 This is a flowchart illustrating the implementation of the present invention;

[0026] Figure 2 This is a schematic diagram of the linear antenna array structure and equivalent source model of the present invention;

[0027] Figure 3 This is a simulation result of the single-section far-field radiation pattern obtained by the present invention. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and specific embodiments:

[0029] Reference Figure 1 The present invention includes the following steps:

[0030] Step 1) Obtain the near-field electric field signal at the operating frequency of the linear array antenna:

[0031] (1a)Reference Figure 2(a) The operating frequency point of the linear array antenna whose initial center is located at the origin of the plane rectangular coordinate system is f0, and the wavelength corresponding to f0 is λ0. The antenna is arranged along the Y direction. The number of antenna elements is determined by the actual type of antenna to be tested. The length of the array antenna is d. In this embodiment, f0 = 10 GHz, λ0 = 0.03 m, and d = 1.2 m.

[0032] (1b) Perform C near-field samplings on the near-field region of the linear array antenna at frequency point f0. The sampling method can be linear sampling, circular sampling, or other planar sampling methods to obtain the discrete electric field signal vector U. C×1 ={U1,U2,...,U c ,...,U C}, where U c This indicates that the c-th coordinate is (x c ,y c The discrete electric field signal corresponding to the sampling point of ) is c∈{1,2,...,C}, where C=51 in this embodiment;

[0033] Step 2) Construct the equivalent source model:

[0034] Reference Figure 2 (b) Construct M, which includes M whose center is located at the origin of the Cartesian coordinate system and is linearly arranged along the Y direction.

[0035] The equivalent source model has m equivalent source points, with an equivalent source model length of d and a spacing of Δλ0 between adjacent equivalent source points. The coordinates of the m-th equivalent source point are (x'...). m ,y' m ), where Δλ0≥0.001λ0, m∈{1,2,...,M}, This indicates rounding up; in this embodiment, Δλ0 = 0.2λ0 = 0.006m, M = 200.

[0036] Step 3) Obtain the correlation coefficient matrix:

[0037] (3a) Through the coordinates (x) of each sampling point c ,y c ) is the coordinates (x') of each equivalent source point. m ,y' m Calculate the distance R from each equivalent source point to each sampling point. c,m The calculation formula is:

[0038]

[0039] (3b) To solve for the equivalent source basis function coefficient vector, it is necessary to use the distance R from each equivalent source point to each sampling point. c,m and related basis functions Λ m Calculate the correlation coefficient A for (x, y).c,m and all correlation coefficients A c,m The combination forms a correlation coefficient matrix A of dimension C×M. C×M The correlation coefficient A c,m The calculation formula is:

[0040]

[0041]

[0042]

[0043] in Indicated by S m The double integral over the boundary, where e denotes the natural logarithm, Λ m (x,y) represents the m-th associated basis function with independent variable coordinates x and y on the x and y axes, respectively. m Represents Λ m Compared to the existing technology that uses a planar equivalent source model, the correlation coefficient matrix obtained by the present invention using a linear equivalent source model has fewer elements and a simpler structure in terms of the distribution region of (x,y).

[0044] Step 4) Obtain the equivalent source basis function coefficient vector:

[0045] For a problem with a finite number of near-field measurement points and an equivalent source constructed using a finite number of basis functions, considering only the radiation of the principal polarization, the near-field problem can be expressed by matrix multiplication. Therefore, the method of moments is adopted, and the discrete electric field signal vector U at the frequency point f0 is used. C×1 With correlation coefficient matrix A C×M Calculate the equivalent source basis function coefficient vector J M×1 The calculation formula is:

[0046] U C×1 =A C×M J M×1

[0047] Compared to existing technologies that use planar equivalent source models, the present invention simplifies the calculation process by eliminating the need for complex matrix-matrix calculations when calculating the equivalent source basis function coefficients.

[0048] Step 5) Obtain the near-field measurement results of a single cross-section of the linear array antenna:

[0049] The construction and description of the equivalent source method can be regarded as a special case of the method of moments in computational electromagnetics. That is, it uses basis functions to expand the equivalent source onto an artificially constructed distribution surface. The solved basis function coefficients describing the distribution of the equivalent source are the unknowns to be solved for the radiation characteristics of the antenna array under test. Therefore, for the equivalent source basis function coefficient vector J... M×1By performing far-field extrapolation, the far-field radiation pattern of a single sectional plane at the center operating frequency can be obtained.

[0050]

[0051] J m J represents the equivalent source basis function coefficient vector. M×1 The coefficients of the m-th equivalent source basis function in the equation.

[0052] The technical effects of the present invention will be explained below with reference to simulation experiments.

[0053] 1. Simulation conditions and content:

[0054] The simulation was performed using the commercial electromagnetic simulation software FEKO.

[0055] The simulation results of the single-section far-field radiation pattern obtained by this invention are as follows: Figure 3 As shown.

[0056] 2. Simulation Result Analysis:

[0057] Reference Figure 3 The horizontal axis represents the angle of the single-plane radiation pattern, and the vertical axis represents the normalized gain value of the single-plane radiation pattern. The solid line in the figure represents the true far-field single-plane radiation pattern, the dotted dashed line represents the single-plane far-field radiation pattern obtained by this method, and the short dashed line below represents the relative error between the single-plane far-field radiation pattern obtained by this method and the true far-field single-plane radiation pattern. It can be seen that the maximum relative error is below -60dB.

[0058] The above description is merely a specific example of the present invention and is only used to illustrate the technical solutions of the present invention. It does not constitute any limitation on the present invention. Obviously, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some or all of the technical features. All such modifications or substitutions under the spirit of the present invention fall within the protection scope of the present invention.

Claims

1. A near-field measurement method for a single-section linear array antenna based on the equivalent source method, characterized in that, Includes the following steps: (1) Obtain the near-field electric field signal at the operating frequency of the linear array antenna: (1a) The operating frequency of the linear array antenna, whose center is located at the origin of the plane rectangular coordinate system and is arranged along the Y direction, is f0, the wavelength corresponding to f0 is λ0, and the length of the linear array antenna is d. (1b) Perform C near-field samplings on the near-field region of the linear array antenna at frequency point f0 to obtain the discrete electric field signal vector U. C×1 ={U1,U2,...,U c ,...,U C }, where U c This indicates that the c-th coordinate is (x c ,y c The discrete electric field signal corresponding to the sampling point of ), c∈{1,2,...,C}; (2) Constructing an equivalent source model: Construct an equivalent source model comprising M equivalent source points centered at the origin of a Cartesian coordinate system and linearly arranged along the Y direction. The distance between adjacent equivalent source points is Δλ0, and the coordinates of the m-th equivalent source point are (x'...). m ,y' m ), where Δλ0≥0.001λ0, m∈{1,2,...,M}, Indicates rounding up; (3) Obtain the correlation coefficient matrix: (3a) Through the coordinates (x) of each sampling point c ,y c ) and the coordinates (x') of each equivalent source point m ,y' m Calculate the distance R from each equivalent source point to each sampling point. c,m ; (3b) The distance R from each equivalent source point to each sampling point c,m and related basis functions Λ m Calculate the correlation coefficient A for (x, y). c,m and all correlation coefficients A c,m The combination forms a correlation coefficient matrix A of dimension C×M. C×M The correlation coefficient A c,m The calculation formula is: in Indicated by S m The double integral over the boundary, where e denotes the natural logarithm, Λ m (x,y) represents the m-th associated basis function with independent variable coordinates x and y on the x and y axes, respectively. m Represents Λ m The distribution region of (x,y); (4) Obtain the equivalent source basis function coefficient vector: The method of moments is employed, and the discrete electric field signal vector U at frequency point f0 is used. C×1 With correlation coefficient matrix A C×M Calculate the equivalent source basis function coefficient vector J M×1 ; (5) Obtain near-field measurement results of a single cross-section of the linear array antenna: For the equivalent source basis function coefficient vector J M×1 Perform far-field extrapolation to obtain polar coordinates with the following values: The far-field radiation pattern of a single tangent at the center working frequency point of the angular coordinate system. Among them, J m J represents the equivalent source basis function coefficient vector. M×1 The coefficients of the m-th equivalent source basis function in the equation.

2. The near-field measurement method for a linear array antenna with a single cross-section based on the equivalent source method according to claim 1, characterized in that, The distance R from each equivalent source point to each sampling point mentioned in step (3a) c,m The calculation formula is:

3. The near-field measurement method for a linear array antenna with a single cut surface based on the equivalent source method according to claim 1, characterized in that, The correlation basis function Λ described in step (3b) m (x, y), its expression is:

4. The near-field measurement method for a linear array antenna with a single cross-section based on the equivalent source method according to claim 1, characterized in that, The calculation of the equivalent source basis function coefficient vector J in step (4) M×1 The calculation formula is: U C×1 =A C×M J M×1 。

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