A method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna in all operating conditions

Abstract

The application discloses a large-scale plane one-way folding array antenna full-working-condition electric performance prediction method, which comprises the following steps: (1) determining a folding position according to a folding angle under different working conditions; (2) determining an array element position after folding according to the folding position and array antenna geometric parameters; and (3) determining a mode excitation coefficient according to each array element position information and single array element mode information, and then calculating electric performance under different working conditions. The application can quickly and accurately analyze folding array antenna radiation and scattering, and has important engineering significance for array antenna analysis and design.

Description

Technical Field

[0001] This invention relates to the field of antenna technology, and specifically to a method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions. Background Technology

[0002] In recent years, with the development of the aerospace field, the application areas and mission complexity of space antennas have gradually increased. However, due to the size limitations of space satellites, antennas cannot be directly launched into space. Therefore, foldable antennas, which can be retracted and deployed, have attracted the attention of researchers. During launch, the foldable antenna is in a retracted state and can be placed in the launch vehicle. At this time, the antenna is small in size and has high rigidity and strength. After entering the space orbit, it unfolds to the intended working position to complete its mission in space. The application of foldable antennas solves the problem of satellite size limitations. The antenna is mounted on the satellite through multiple connecting arms and deployment joints. Installation errors and deployment errors of various components of the system can cause deviations in the antenna's position and attitude accuracy, thus affecting its electrical performance. Therefore, studying the mechanism by which position and attitude errors affect the electrical performance of foldable antennas is crucial for predicting their on-orbit electrical performance and eliminating errors.

[0003] The impact of position and attitude errors on the electrical performance of folded arrays can be categorized as an electromechanical coupling problem of array antennas. Two key aspects of this problem are the accuracy and efficiency of the coupling model. Currently, the pattern product theorem is mainly used for analyzing the electrical performance of deformable array antennas. For example, Schippers et al. studied the influence of structural deformation on the radiation pattern of a conformal phased array antenna based on this theorem. While the pattern product theorem is concise, it completely ignores the mutual coupling effect between array elements, leading to insufficient accuracy in the analysis results. Some full-wave analysis methods, such as the method of moments, the finite element method, and the finite-difference time-domain method, construct algebraic equations based on the electromagnetic field control equations and boundary conditions for accurate analysis of array antenna electrical performance. However, these are general-purpose methods that do not reflect the electromechanical coupling characteristics of array antennas and involve very large computational loads. Summary of the Invention

[0004] To overcome the shortcomings of the above technologies, the present invention aims to provide a method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions. This method considers the mutual coupling effect between array elements, the offset error of array elements, and the attitude deflection error, and can accurately and quickly analyze the radiation field of the folded array antenna. It is of great significance for predicting the electrical performance of deformable array antennas in practical engineering.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions includes the following steps;

[0007] (1) Determine the crease position according to the folding angle under different working conditions;

[0008] (2) Determine the position of the array elements after folding based on the crease position and the array antenna geometry parameters;

[0009] (3) Determine the mode excitation coefficient based on the position information of each array element and the mode information of a single array element, and then calculate the electrical performance under different operating conditions.

[0010] In step (1), the crease position is determined according to the following steps:

[0011] (1a) Let the edges of the planar array along the non-folded direction and the folded direction be the X-axis and the Y-axis, respectively. Fix the edges along the X-axis, and let each crease be parallel to the X-axis. Let the projection point of the i-th crease onto the YOZ plane be (0, Y). i Z i The folding angle of the i-th column is θ. i (Folding upwards is positive, folding downwards is negative), then the projection point of the (i+1)th crease on the YOZ plane is (0, Y). i+1 Z i+1 )for

[0012]

[0013] in,

[0014] Let be the rotation matrix about the X-axis, and l be the width of each column.

[0015] In step (2), the positions of the array elements under different working conditions are determined based on the crease positions determined in step (1), and the following steps are followed:

[0016] (2a) The integration point on the i-th column element is:

[0017]

[0018] Among them, (x i ,y i ,z i Let be the coordinates of the integration points of the ideal array elements. Given the coordinates of the integration points of the ideal array elements and the spacing between array elements, the coordinates of the integration points of all array elements under different operating conditions can be obtained from the above formula.

[0019] In step (3), based on the array element integration point positions obtained in step (2), the mode excitation coefficients are determined and the electrical performance under different operating conditions is calculated, following these steps:

[0020] (3a) The mode excitation coefficient matrix V of the array is

[0021] V=(U-CΛ) -1 V0

[0022] Where V0 is the column matrix composed of the initial mode excitation coefficients of each element of the array antenna, Λ is the diagonal matrix of the element eigenvalues, U is the identity matrix, and C is the mode coupling matrix, obtained by the following formula.

[0023]

[0024]

[0025] ω is the mode coupling coefficient; μ is the electromagnetic wave angular frequency; μ is the free space permeability. These are the a-th mode current of the m-th element and the b-th mode current of the n-th element, respectively. Let r be a scalar Green's function, and r' and r' be the position vectors of the integration points on the m-th and n-th array elements, respectively, obtained from step (2);

[0026] (3b) The electrical performance under different operating conditions can be obtained from the far-field radiation pattern function F(θ,φ) of the array antenna. F(θ,φ) can be expressed as a linear combination of the electric fields of each array element mode, and its calculation formula is as follows:

[0027] F(θ,φ)=ΠΛ(U-CΛ) -1 V0

[0028] In the formula, Π is the array of far-field modes composed of each element of the array antenna, and (θ,φ) is the observation angle.

[0029] The beneficial effects of this invention are:

[0030] 1. In practical engineering, accurate analysis of the electrical performance of deformable array antennas is of great significance. This invention proposes a method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions. Starting from the radiation characteristics of isolated array elements, a correlation model is constructed between the radiation characteristics of array elements and the total radiation characteristics of the folded array antenna, which has important guiding significance for the analysis and design of folded array antennas.

[0031] 2. Compared with traditional methods for analyzing the electrical performance of deformable array antennas, this invention considers both translational and rotational deformation of array elements, and only requires calculation of the characteristic modes of a single array element. Compared with commercial software FEKO, it accelerates the calculation speed and can accurately and quickly analyze the electrical performance of array antennas. Attached image description:

[0032] Figure 1 This is a flowchart of a method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions, according to the present invention.

[0033] Figure 2It has three states: fully unfolded, intermediate state, and fully collapsed.

[0034] Figure 3 This refers to the ideal operating state and element information of the butterfly array antenna;

[0035] Figure 4 These are two array sizes under operating condition I;

[0036] Figure 5 These are two array sizes under Condition II;

[0037] Figure 6 This is a comparison of the radiation pattern of the 5×6 array in case I using the present invention and the simulation results of the commercial software FEKO.

[0038] Figure 7 This is a comparison of the radiation pattern of the 50×6 array under condition I using the present invention and the simulation results of the commercial software FEKO.

[0039] Figure 8 This is a comparison of the radiation pattern of the 5×6 array under condition II using the present invention and the simulation results of the commercial software FEKO.

[0040] Figure 9 This is a comparison of the radiation pattern of the 50×6 array under operating condition II using this invention and the simulation results of the commercial software FEKO. Detailed Implementation

[0041] The present invention will be further described in detail below with reference to the embodiments.

[0042] Reference Figure 1 This invention provides a method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions. The specific steps are as follows:

[0043] Step 1, determine the crease location

[0044] Determining the crease location based on the folding angle under different working conditions includes the following steps:

[0045] (1a) Let the edges of the planar array along the non-folded direction and the folded direction be the X-axis and the Y-axis, respectively, and fix the edge along the X-axis. Each crease is parallel to the X-axis. Let the projection point of the i-th crease onto the YOZ plane be (0, Y). i Z i The folding angle of the i-th column is θ. i (Folding upwards is positive, folding downwards is negative), then the projection point of the (i+1)th crease on the YOZ plane is (0, Y). i+1 Z i+1 )for

[0046]

[0047] in, Let be the rotation matrix about the X-axis, and l be the width of each column.

[0048] Step 2, determine the position of the array elements

[0049] Based on the crease positions determined in step 1, the positions of the array elements under different working conditions are determined, including the following steps:

[0050] (2a) The integration point on the i-th column element is:

[0051]

[0052] Among them, (x i ,y i ,z i Let be the coordinates of the integration points of the ideal array elements. Given the coordinates of the integration points of the ideal array elements and the spacing between array elements, the coordinates of the integration points of all array elements under different operating conditions can be obtained from the above formula.

[0053] Step 3: Solve for the array mode excitation coefficient matrix and the electrical performance under different operating conditions.

[0054] Based on the array element integration point positions obtained in step 2, the mode excitation coefficient matrix and electrical performance of the array antenna are determined, including the following steps:

[0055] (3a) Determine the mode excitation coefficients of array element m in the array environment:

[0056]

[0057] In the formula, M is the total number of array elements, and N is the total number of array elements. n Let n be the number of pattern cutoffs for array element n. These are the b-th order eigenvalue and mode excitation coefficient of array element n, respectively. Let be the excitation coefficient of the a-th order initial mode of array element m, which can be calculated by the following formula:

[0058]

[0059] The mode coupling coefficient can be calculated using the following formula:

[0060]

[0061] In the formula, Let n be the b-th order mode electric field of array element n.

[0062] (3b) Repeat step (3a) to obtain the equilibrium equations satisfied by all orders of modes of array element m, as follows:

[0063]

[0064] In the formula

[0065]

[0066]

[0067]

[0068]

[0069] In the formula, the superscript T denotes the transpose operation, and the operator diag generates a diagonal matrix with the input parameters as diagonal elements. m V n These are arrays of mode excitation coefficients for array elements m and n, respectively. C is the initial mode excitation coefficient array for this array element. mn Let Λ be the mode coupling matrix of array element n against array element m. n It is a diagonal matrix with respect to the eigenvalues ​​of the array element n;

[0070] (3c) Repeat step (3b) for all elements in the array to obtain the coupling balance equation satisfied by the mode excitation coefficients of each element, strictly considering the mutual coupling effect:

[0071] V = V0 + CΛV

[0072] In the formula

[0073]

[0074]

[0075]

[0076] Λ = diag(Λ) n )

[0077] In the formula, V is the array of mode excitation coefficients of each element of the array antenna, V0 is the array of initial mode excitation coefficients of each element of the array antenna, C is the mode coupling matrix, and Λ is the diagonal matrix with respect to the eigenvalues ​​of each element of the array antenna.

[0078] (3d) Solving the coupling equilibrium equation established in step (3c) yields the mode excitation coefficients V for each element in the array environment:

[0079] V=(U-CΛ) -1 V0

[0080] The mode coupling coefficient can be written as:

[0081]

[0082]

[0083] ω is the angular frequency of the electromagnetic wave, and μ is the permeability of free space. These are the a-th mode current of the m-th element and the b-th mode current of the n-th element, respectively. Let r be a scalar Green's function, and r' and r' be the position vectors of the integration points on the m-th and n-th array elements, respectively, obtained from step (2).

[0084] (3e) Based on the element mode excitation coefficients obtained in step (3d), determine the element mode weight coefficients as follows:

[0085] P = ΛV = Λ(U - CΛ) -1 V0

[0086] (3f) The electrical performance under different operating conditions can be represented by the far-field radiation pattern function F(θ,φ) of the array antenna. F(θ,φ) can be expressed as a linear combination of the electric fields of each array element mode, and its calculation formula is as follows:

[0087] F(θ,φ)=ΠP=ΠΛ(U-CΛ) -1 V0

[0088] In the formula

[0089]

[0090]

[0091] In the formula, P is the array composed of the weighted coefficients of the modes of each element of the array antenna, Π is the array composed of the far-field modes of each element of the array antenna, and k is the electromagnetic wave propagation constant. For the far field of the a-th mode of array element m, r m Let (θ, φ) be the position vector of array element m, and (θ, φ) be the observation angle.

[0092] The advantages of this invention can be further illustrated by the following simulation examples.

[0093] 1. Simulation parameters

[0094] Taking a butterfly-shaped radiating element with a center operating frequency of f = 2 GHz and the folded array antenna it forms as an analysis case, the three states of the array are as follows: Figure 2 As shown, the ideal array arrangement and element structure dimensions are as follows: Figure 3 As shown, in array case I, the folding angle of each column is the same, such as... Figure 4 As shown, the folding angle of each column in array case II is different, such as... Figure 5 As shown.

[0095] 2. Simulation Content and Results

[0096] Figures 6-9 Far-field radiation pattern curves under two operating conditions are presented. It can be seen that the present invention can accurately analyze the radiation performance of the array antenna, and the results are consistent with those of the commercial software FEKO, verifying the effectiveness of the method. Table 1 shows a comparison of the computation time of the present invention and the commercial software FEKO, demonstrating that the present invention has a shorter computation time, and this advantage becomes more pronounced as the array size increases.

[0097] Table 1: Comparison of computation time between the present invention and the commercial software FEKO

[0098]

[0099] This invention is not limited to the above-described embodiments. Based on the technical solutions disclosed in this invention, those skilled in the art can make some substitutions and modifications to some of the technical features without creative effort, and all such substitutions and modifications are within the protection scope of this invention.

Claims

1. A method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions, characterized in that, Includes the following steps; (1) Determine the crease position based on the folding angle under different working conditions; (2) Determine the position of the array elements after folding based on the crease position and the array antenna geometry parameters; (3) Determine the mode excitation coefficients based on the position information of each array element and the mode information of a single array element, and then calculate the electrical performance under different operating conditions; In step (2), the positions of the array elements under different working conditions are determined based on the crease positions determined in step (1), and the following steps are followed: (2a) i The integration point on the array element is in, Given the coordinates of the integration points of the ideal array elements and the spacing between array elements, the above formula can be used to obtain the integration point coordinates of all array elements under different operating conditions. In step (3), based on the array element integration point positions obtained in step (2), the mode excitation coefficients are determined and the electrical performance under different operating conditions is calculated, following these steps: (3a) Mode excitation coefficient matrix of the array for in, It is an array composed of the initial mode excitation coefficients of each element of the array antenna. The diagonal matrix of eigenvalues ​​of the array elements. It is the identity matrix. The mode coupling matrix is ​​obtained from the following formula. These are the mode coupling coefficients; The angular frequency of electromagnetic waves Permeability in free space , They are the first m Individual Element a First-order mode current and the first-order mode current n Each formation element b First-mode current, For scalar Green's function, , The first m The and the first n The position vectors of the integration points on each array element are obtained from step (2); (3b) The electrical performance under different operating conditions can be obtained from the far-field radiation pattern function of the array antenna. get, It can be expressed as a linear combination of the electric fields of each array element mode, and its calculation formula is as follows: In the formula, An array composed of the far-field modes of each element of the array antenna. This is the observation angle.

2. The method for predicting the electrical performance of a large-scale planar unidirectional folded array antenna under all operating conditions according to claim 1, characterized in that, In step (1), the crease position is determined according to the following steps: (1a) Let the non-folded direction and the folded direction of the planar array be the X-axis and the Y-axis, respectively. Fix the edge on the X-axis, and let each crease be parallel to the X-axis. Let the first crease be the first crease. i The projection point of the crease on the YOZ plane is... , No. i The folding angle of the column is Folding upwards is positive, folding downwards is negative, then the first... i+ The projection point of a crease on the YOZ plane for in, , Let X be the rotation matrix about the X-axis. l The width of each column.

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