Method for quickly estimating electrical performance of large foldable array antenna under full working conditions

Abstract

The invention discloses a large-scale foldable array antenna full-condition electrical performance rapid estimation method. The method comprises the following steps: determining folding structure parameters of a folding array antenna configuration; calculating a corner relation between the basic folding units, determining an array element center point position vector and a rotation matrix of the folding array antenna under different unfolding working conditions, and further determining a position vector of an array area division point and a mode excitation coefficient matrix and a mode coupling matrix of the folding array antenna under different folding conditions; and calculating a far-field pattern of the foldable array antenna under each working condition, and quickly estimating the electrical performance of the foldable array antenna under the full working condition. According to the method, the structure parameterization characterization and electrical property rapid calculation of the two-dimensional folded array antenna can be completed, and the problem that the calculation precision is low due to the fact that an existing far-field estimation method is unclear in characterization of the mutual coupling effect of array elements in the array antenna is effectively solved.

Description

Technical Field

[0001] The present invention belongs to the field of antenna technology, and specifically relates to a method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions. The method can be used to guide the modeling of large foldable antennas in actual work and the rapid estimation of electrical performance under non-ideal working conditions. Background Art

[0002] A foldable antenna is an antenna structure that researchers have applied to antenna systems using origami models. The SeaSat-SAR satellite, launched in 1978 by NASA's Jet Propulsion Laboratory, carried a one-dimensional foldable antenna consisting of 16 foldable antenna panels. Compared to one-dimensional folding antennas, two-dimensional foldable antennas have antenna units that can fold and unfold in both directions, achieving a larger folding and unfolding ratio and enabling more reliable, convenient, and economical transportation. The modeling concept for two-dimensional array antennas is derived from the origami model, which transforms the two-dimensional origami model into a three-dimensional spatially deployable structure. Through rigorous geometric calculations and motion analysis, the position information of the origami structure's paper surface in different folded states can be obtained. By characterizing the characteristics of the paper surface in the folded state, the position and attitude changes of the two-dimensional folding antenna during the folding and unfolding process can be described, allowing for accurate calculation of the electrical performance of the folding array antenna in actual operation when the folding antenna is incompletely unfolded due to factors such as unfolding errors.

[0003] Current research on foldable antennas focuses on two key areas, given their unique characteristics. The first is the design of the antenna's folding structure. For example, the sunflower-shaped fixed-surface deployment mechanism developed by TRW (USA) boasts high deployment accuracy. The DAISY deployment mechanism developed by Dornier and ESA offers high reliability. The second is addressing electromagnetic calculations for incompletely deployed foldable antennas. The main reason for the deterioration in the electrical performance of two-dimensional folded antennas is that the antenna elements change in position and orientation, affecting the mutual coupling between elements, the spatial phase during radiation, and the antenna's orientation. The traditional pattern product theorem currently describes the influence of antenna element position on phased array radiation performance, but it does not consider the mutual coupling between antenna elements. To address this issue, DMPozar proposed an active element pattern that directly superimposes active element patterns. However, obtaining active element patterns typically requires extensive simulation or experimentation, which is time-consuming and expensive. Furthermore, deformation of the antenna will also alter the active element pattern. The active element method ignores the effects of these deformations on the antenna's far field, resulting in inaccurate calculations. While traditional full-wave algorithms can provide accurate calculations, they are time-consuming. As shown above, the structural and electromagnetic aspects of folded antenna research are typically conducted separately. Integrating structural modeling and electromagnetic calculations allows for rapid analysis of the antenna array's far-field radiation under various operating conditions, reducing analysis and calculation time and having significant engineering significance. Summary of the Invention

[0004] To address the aforementioned shortcomings of the prior art, the present invention aims to provide a method for rapidly estimating the electrical performance of a large foldable array antenna under all operating conditions. This method utilizes a Miura folding configuration, completing structural modeling of the Miura folded array antenna under various operating conditions while enabling more accurate and rapid calculation of the antenna's far-field radiation, taking mutual coupling effects into account. This method not only achieves high computational accuracy, but also significantly reduces the time required to calculate the folded antenna's far-field radiation under various unexpected operating conditions compared to traditional full-wave algorithms, thus possessing significant engineering value.

[0005] The present invention is achieved through the following technical solutions.

[0006] The present invention provides a method for rapidly estimating the electrical performance of a large foldable array antenna under all operating conditions, comprising:

[0007] Determine the folding structure parameters of the folded array antenna configuration;

[0008] According to the folding structure parameters, the relationship between the edges and angles of the basic folding units is calculated to determine the position vector and rotation matrix of the center point of the folded array antenna under different unfolding conditions;

[0009] Determine the position vector of the array surface integral point according to the position vector of the array element center point and the rotation matrix;

[0010] According to the position vector of the array surface integral point, the mode excitation coefficient matrix and mode coupling matrix of the folded array antenna under different folding conditions are determined to characterize the mutual coupling effect of the array surface under different states;

[0011] According to the mutual coupling effect under different states, the far-field radiation pattern of the foldable array antenna under various working conditions is calculated, and the electrical performance of the foldable array antenna under all working conditions is quickly estimated.

[0012] Preferably, the folding array antenna is configured as a Miura folding structure, and the folding method is to open and close by stretching the diagonal line;

[0013] The folding structural parameters of the folded array antenna configuration are determined, including: the dihedral angle folding angle θ between two adjacent surfaces of the valley fold; the side lengths a and b of the two sides of the unit, and the angle α between a and b.

[0014] Preferably, calculating the relationship between the edges and angles of the basic folding units includes:

[0015] Set one vertex of the basic folding unit as the coordinate axis vertex, the coordinate axis parallel to the valley fold as the X axis, the coordinate axis parallel to the two peak folds as the Y axis, and the coordinate axis perpendicular to the XY plane as the Z axis;

[0016] The folding angles corresponding to the creases in the Y-axis definition direction are equal;

[0017] Calculate the angles between the edges of the folded units on the XZ plane and the angles between the edges of the folded units on the XY plane;

[0018] According to the angles between the edges of the folding units on the XZ plane and the angles between the edges of the folding units on the XY plane, calculate the distances BD and BH between the intersection points of the valley crease and the peak crease corresponding to the paper surface on the XY coordinate plane under different folding states: calculate the angle between the paper surface corresponding to the peak crease and the horizontal plane.

[0019] Preferably, determining the position vector and rotation matrix of the center point of the folded array antenna under different unfolding conditions includes:

[0020] Calculate the position vector of the center point of the array element through the position vector of the center point of the array element on the basic folding unit;

[0021] The array element center position vector is obtained by the array element center position vector when the array element index numbers p and q are both odd, the array element center position vector when the array element index number p is even and q is odd, the array element center position vector when the array element index number p is odd and q is even, and the array element center position vector when the array element index numbers p and q are both even;

[0022] Calculate the array element rotation matrix according to the position vector of the array element center point;

[0023] The array element rotation matrix is obtained by the array element rotation matrix where the array element index numbers p and q are both odd, the array element rotation matrix where the array element index number p is even and q is odd, the array element rotation matrix where the array element index number p is odd and q is even, and the array element rotation matrix where the array element index numbers p and q are both even.

[0024] Preferably, the position vectors of the array surface integral points are determined, and the position vectors of all integral points on the entire array surface are calculated using homogeneous transformation according to the position vector of the array element center point and the relative position vector of the array element integral point relative to the center point.

[0025] Preferably, determining the mode excitation coefficient matrix and the mode coupling matrix of the folded array antenna under different folding conditions includes:

[0026] According to the position vector of the obtained integral point, the coupling coefficients of each order mode of each element of the array antenna under different working conditions are obtained;

[0027] Calculate the mode excitation coefficient based on the mode coupling coefficient;

[0028] According to the mode coupling coefficient and the mode excitation coefficient, the mode excitation coefficient matrix and the mode coupling matrix are calculated.

[0029] Compared with the prior art, the present invention has the following beneficial effects:

[0030] 1. Compared with the existing technology that focuses on the reliability characteristics of the antenna structure design for folding antennas, the present invention proposes a method for quickly calculating the electrical performance of the folding antenna due to hinge failure. By changing the folding parameters and structural parameters, the far-field radiation pattern of the foldable array antenna under various working conditions can be quickly calculated.

[0031] 2. The method of the present invention effectively solves the problems of the existing electromagnetic calculation methods in calculating the electrical performance of folded array antennas, such as long time consumption and complex operation. On the one hand, the present invention uses folding parameters and structural parameters to describe the various states of the folded array antenna, and calculates the position vector and rotation matrix of the center point of the array element of the folded array antenna under different unfolding conditions, which are used to represent the position and posture of each antenna element in each state; on the other hand, by calculating the mode excitation coefficient matrix and mode coupling matrix of the folded array antenna under different folding conditions, the mutual coupling effect of the array surface in different states is characterized, and the field superposition principle is used to calculate the far-field radiation pattern of the folded array antenna under various working conditions, which effectively solves the problem of low calculation accuracy caused by the unclear characterization of the mutual coupling effect of the array elements in the array antenna by the existing far-field prediction method. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The drawings described herein are used to provide a further understanding of the present invention, constitute a part of this application, and do not constitute an improper limitation of the present invention. In the drawings:

[0033] Figure 1 This is a flow chart of a method for rapidly estimating the electrical performance of a large foldable array antenna under all operating conditions;

[0034] Figure 2 It is the intention of Miura folding to show;

[0035] Figure 3 It is a schematic diagram of the Miura folding unit structure;

[0036] Figure 4 is the modeling diagram of the folded antenna when the structural parameter is τ1;

[0037] Figure 5 The modeling diagram of the folded antenna when the structural parameter is τ2;

[0038] Figure 6 This is a comparison chart of FEKO calculation and model calculation under three working conditions of the structural parameter τ1 folded antenna;

[0039] Figure 7 This is a comparison chart of FEKO calculation and model calculation under three working conditions of the structural parameter τ2 folded antenna;

[0040] Figure 8 This is a diagram showing the influence of the folding angle on the electric field radiated by the antenna. DETAILED DESCRIPTION

[0041] The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments. The exemplary embodiments and descriptions of the present invention are used to explain the present invention but are not intended to limit the present invention.

[0042] Reference Figure 1 The present invention provides a method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions. The specific steps are as follows:

[0043] Step 1: Determine the folding structure parameters of the folded array antenna configuration.

[0044] The folding configuration of the present invention is Miura folding. The folding method of this origami structure is to stretch the diagonal line to achieve opening and closing. The folding design of this folding structure can greatly compress the structural space and has a large folding and unfolding ratio. The folding and unfolding process is as follows: Figure 2 As shown in Figure 2, due to the single degree of freedom of the folding method, only one folding angle needs to be defined to characterize the wrinkle state of the entire array.

[0045] For ease of calculation, the present invention uses the dihedral angle between two adjacent faces of a valley fold as the folding angle, denoted as θ, to represent the single degree of freedom of the Miura fold structure. The lengths of the two sides of the unit cell are set to a and b, and the angle between a and b is α.

[0046] Step 2: Calculate the edge-angle relationship between basic folding units based on the folding structure parameters.

[0047] The specific steps include:

[0048] Assume that one vertex of the basic folding unit is the coordinate axis, the coordinate axis parallel to the valley fold is the X axis, the coordinate axis parallel to the two peak folds is the Y axis, and the coordinate axis perpendicular to the XY plane is the Z axis. For the convenience of the following description, the numbering of each vertex is as follows Figure 3 As shown. According to the folding properties, the folding angles corresponding to the creases in the Y-axis direction are equal. The angles between the edges of the folding units on the XZ plane and the angles between the edges of the folding units on the XY plane are defined as θ1 and θ2. Based on the motion relationship and structural characteristics of the folding units, the calculation formulas for θ1 and θ2 are:

[0049] According to the folding unit motion relationship and structural characteristics, the angle θ1 between the folding unit edges on the XZ plane and the angle θ2 between the folding unit edges on the XY plane are calculated. The calculation formula is:

[0050]

[0051] cos(θ2)=sin 2 α·cosθ+cos 2 α

[0052] Where: α is the angle between sides a and b, and θ is the folding angle of the folding unit.

[0053] According to the angles between the edges of the folding units on the XZ plane and the angles between the edges of the folding units on the XY plane, calculate the distances BD and BH between the intersection points of the valley folds and peak folds corresponding to the paper surface on the XY coordinate plane under different folding states:

[0054] BH=l1=2a·sin(θ1 / 2)

[0055] BD=l2=2b·sin(θ2 / 2)

[0056] Calculate the angle γ between the peak fold and the horizontal plane, and the angle β between the peak fold in the Y direction and the paper surface. The calculation formulas are:

[0057] β=cos -1 [1-2cot 2 αtan 2 (θ2 / 2)]

[0058] γ=cos -1 (l1 / 2a)

[0059] Where: a is the side length of the paper, and α is the angle between the two sides of the paper.

[0060] Step 3: Calculate the position vector and rotation matrix of the center point of the folded array antenna under different unfolding conditions to determine the position and posture of the array antenna under different conditions.

[0061] Calculating the position of the center point of the array element and the rotation matrix of each array element based on the edge-angle relationship of the folding unit obtained in step 2 includes the following steps:

[0062] (3a) The position vector of the center point of the array element can be calculated by the position vector of the center point of the array element on the basic folding unit. The calculation formula of the position vector of the center point of the array element on the entire array surface is:

[0063]

[0064] Where (a) is the calculation formula for the position vector of the center point of the array element when the array element index numbers p and q are both odd numbers. (b) is the calculation formula for the position vector of the center point of the array element when the array element index number p is even and q is odd. (c) is the calculation formula for the position vector of the center point of the array element when the array element index number p is odd and q is even. (d) is the calculation formula for the position vector of the center point of the array element when the array element index numbers p and q are both even numbers. f(p,q,τ,θ) is the position vector function of the center point of the array element when the row index number is p and the column index number is q, and is a function of the structural parameter τ and the folding parameter θ. pq is the position vector of the array element at row index p and column index q, l1 and l2 are the BD and BH lengths calculated in step 3 respectively.

[0065] (3b) Calculate the array element rotation matrix

[0066] The rotation matrix of each array element can be obtained by folding the unit relationship. According to the dihedral angle relationship between each folded unit face, the rotation matrix of the array element is calculated as follows:

[0067]

[0068] Where (a) is the calculation formula for the array element rotation matrix when the array element index numbers p and q are both odd. (b) is the calculation formula for the array element rotation matrix when the array element index number p is even and q is odd. (c) is the calculation formula for the array element rotation matrix when the array element index number p is odd and q is even. (d) is the calculation formula for the array element rotation matrix when the array element index numbers p and q are both even. T a The rotation matrix represents the rotation about the a-axis. Given the axis and angle of rotation, it can be calculated using the Rodriguez rotation formula. T(p,q,τ,θ) is the rotation matrix function for the element at row index p and column index q.

[0069] According to the rotation matrix of the array element, the position and posture of the array antenna under different working conditions are determined.

[0070] Step 4: Determine the position vector of the array surface integral point based on the position vector of the array element and the rotation matrix.

[0071] Based on the position vector of the array element center point and the rotation matrix of the array element obtained in step 3, the position vectors of the array surface integral points under different states are calculated, including the following steps:

[0072] According to the position vector of the center point of the array element and the relative position vector of the array element integration point relative to the center point, the position vector of all integration points on the entire array surface can be calculated using homogeneous transformation. The calculation formula is:

[0073] r d (τ,θ)=T(p,q,τ,θ)·r+f(p,q,τ,θ)

[0074] where r d (τ,θ) represents the position vector of each integration point, which is a function of the structural variable τ and the folding parameter θ. r is the position vector of the integration point relative to the center point of the array element. f(p,q,τ,θ) is the position vector of the center point of the array element calculated in step 4. T(p,q,τ,θ) is the rotation matrix of each array element.

[0075] Step 5: Calculate the mode excitation coefficient matrix and mode coupling matrix of the folded array antenna under different folding conditions to characterize the mutual coupling effect of the array under different states.

[0076] The specific steps include:

[0077] (5a) The integral point position vector r calculated according to step 4 d (τ,θ M ), calculate the mode coupling coefficient, which is calculated as follows:

[0078]

[0079] Where: j is the imaginary unit, ω is the angular frequency of the electromagnetic wave, μ is the magnetic permeability of free space, S m is the integration domain of array element m, S n is the integration domain of array element n, The relationship between the a-order mode current of element m and the b-order mode current of element n is represented by r. d (τ,θ M ) is the position vector of the integration point on the m radiation unit on the folded array when the folding angle is θ, r′ d (τ,θ M ) is the position vector of the integration point on the n radiation unit on the folded array when the folding angle is θ. At this time, the integration point on the m radiation unit is the field point, and the integration point on the n radiation unit is the source point. G(r d (τ,θ),r′ d(τ,θ)) is the Green function, are the a-order mode current of the m-th array element and the b-order mode current of the n-th array element, k is the free space wave number, ▽ s , ▽′ are the Hamiltonian operator and the two-dimensional Hamiltonian operator respectively.

[0080] (5b) Calculate the a-order mode excitation coefficient of array element m:

[0081]

[0082] in, is the a-order mode excitation coefficient of array element m, is the a-order initial mode excitation coefficient of array element m, is the mode coupling coefficient under different working conditions, which characterizes the mutual coupling effect of array elements n and m in a and b modes, N is the number of array elements, λ b is the b-th order eigenvalue, is the mode coupling matrix of array element n to array element m in the a-order mode, Γ n Represents the excitation coefficient matrix of each order mode of array element n, Λ n is a diagonal matrix of eigenvalues of array element n.

[0083] (5b) The calculation formula for the excitation coefficient of each order mode of array element m is:

[0084]

[0085] …

[0086]

[0087] Written in matrix form:

[0088]

[0089] Where:

[0090]

[0091] Where: (C mn ) Miura is the mode coupling matrix of array element n to array element m in each state.

[0092] (5c) Calculate the mode coupling matrix and mode excitation coefficient matrix

[0093] Repeat (5b) to derive the excitation coefficient matrix and mode coupling matrix of all array elements, and the relationship is:

[0094] Γ=Γ 0 +ΓΛC Miura

[0095] Where:

[0096] Γ 0 =[Γ 10 Γ 20 … Γ N0 ] T

[0097]

[0098] Where: Γ mode excitation coefficient matrix, Γ 0 is the array of initial mode excitation coefficients of each element of the array antenna, Λ is the diagonal matrix of the eigenvalues of each element of the array antenna, C Miura is the mode coupling matrix of the folded array.

[0099] Step 6: Calculate the far-field radiation pattern of the folded array antenna under various working conditions.

[0100] According to the mode excitation coefficient and mode coupling matrix obtained in step 5, the mode weighting coefficient is obtained, and the far-field radiation pattern of the folded array antenna under various working conditions is calculated, including the following steps:

[0101] (6a) Calculate the mode weight matrix

[0102] Α=ΓΛ=Γ0(UC Mirua Λ) -1 Λ

[0103] (6b) Calculate the far-field pattern of the folded array antenna

[0104] The far-field pattern is calculated using the electric field superposition principle, and the calculation formula is:

[0105]

[0106] Where: ω is the angular frequency of the electromagnetic wave, μ is the free space magnetic permeability, r is the distance of the observation point, k is the free space wave number, U is the unit matrix, and F is the far-field pattern matrix of each antenna of the folded array antenna after the spatial phase term and antenna pointing change due to the change of antenna position.

[0107] The electrical performance of the foldable array antenna under all working conditions is quickly estimated based on the far-field radiation pattern.

[0108] The advantages of the present invention can be further illustrated by the following simulation case.

[0109] 1. Simulation parameters

[0110] refer to Figure 4 and Figure 5The simulation of the present invention uses arrays with structural parameters of τ1 and τ2 for comparative calculation. In τ1, a = b = 60 mm, α = 70 degrees, and the number of array elements in the X and Y directions is 8. In τ2, a = b = 80 mm, α = 60 degrees, and the number of array elements in the X direction and the Y direction is 18, and the number of array elements in the Y direction is 14. The antenna units are all butterfly antennas with a frequency of 2 GHz. The radiation far field is calculated when the folding angle θ is 180°, 150°, and 120° respectively.

[0111] 2. Simulation content and results

[0112] Figure 6 and Figure 7 The results of calculation using the moment method and the model of the present invention are compared. By comparing the results of the two curves, the results of the far field calculated by the two methods are basically consistent at the phi=0 and phi=90 sections. Figure 8 A comparison diagram of the far field calculated at different folding angles using this model is provided. This model can clearly analyze the impact of the folding angle on the electrical performance of the antenna.

[0113] Table 1 is a comparison of the calculation time of the model used in the present invention and the traditional full-wave algorithm moment method

[0114] Table 1 Comparison of calculation time

[0115]

[0116] From the calculation time consumption of folded array antennas of two different sizes at several different folding angles, it can be seen that the higher the folding degree, the longer the calculation time consumption, and as the scale increases, the calculation advantage of the calculation method of the present invention over the moment method becomes greater.

[0117] From this, it can be seen that the calculation method of the present invention ensures high accuracy when calculating the electrical performance of the folded array antenna under different working conditions, and the efficiency is also greatly improved when performing calculations on large array antennas, providing an effective implementation approach for solving the problem of quickly calculating the electrical performance of the folded array antenna under various unfolding working conditions in engineering.

[0118] The present invention is not limited to the above-mentioned embodiments. On the basis of the technical solutions disclosed in the present invention, those skilled in the art can make some substitutions and modifications to some of the technical features therein according to the disclosed technical content without creative labor, and these substitutions and modifications are all within the protection scope of the present invention.

Claims

1. A method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions, characterized in that: include: Determine the folding structure parameters of the folded array antenna configuration; According to the folding structure parameters, the relationship between the edges and angles of the basic folding units is calculated to determine the position vector and rotation matrix of the center point of the folded array antenna under different unfolding conditions; Determine the position vector of the array surface integral point according to the position vector of the array element center point and the rotation matrix; According to the position vector of the array surface integral point, the mode excitation coefficient matrix and mode coupling matrix of the folded array antenna under different folding conditions are determined to characterize the mutual coupling effect of the array surface under different states; According to the mutual coupling effect under different states, the far-field radiation pattern of the foldable array antenna under various working conditions is calculated, and the electrical performance of the foldable array antenna under all working conditions is quickly estimated.

2. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 1 is characterized in that: The folding array antenna has a Miura folding structure, and the folding method is to open and close by stretching the diagonal line; Determine the folding structural parameters of the folded array antenna configuration, including: the dihedral folding angle θ of two adjacent faces of the valley fold; The lengths of the two sides of the unit are a, b, and the angle α between a, b.

3. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 1 is characterized in that: Calculate the edge-angle relationship between basic folding units, including: Set one vertex of the basic folding unit as the coordinate axis vertex, the coordinate axis parallel to the valley fold as the X axis, the coordinate axis parallel to the two peak folds as the Y axis, and the coordinate axis perpendicular to the XY plane as the Z axis; The folding angles corresponding to the creases in the Y-axis definition direction are equal; Calculate the angles between the edges of the folded units on the XZ plane and the angles between the edges of the folded units on the XY plane; According to the angles between the edges of the folding units on the XZ plane and the angles between the edges of the folding units on the XY plane, calculate the distances BD and BH between the intersection points of the valley crease and the peak crease corresponding to the paper surface on the XY coordinate plane under different folding states: calculate the angle between the paper surface corresponding to the peak crease and the horizontal plane.

4. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 1 is characterized in that: Determine the position vector and rotation matrix of the element center point of the folded array antenna under different unfolding conditions, including: Calculate the position vector of the center point of the array element through the position vector of the center point of the array element on the basic folding unit; The array element center position vector is obtained by the array element center position vector when the array element index numbers p and q are both odd, the array element center position vector when the array element index number p is even and q is odd, the array element center position vector when the array element index number p is odd and q is even, and the array element center position vector when the array element index numbers p and q are both even; Calculate the array element rotation matrix according to the position vector of the array element center point; The array element rotation matrix is obtained by the array element rotation matrix where the array element index numbers p and q are both odd, the array element rotation matrix where the array element index number p is even and q is odd, the array element rotation matrix where the array element index number p is odd and q is even, and the array element rotation matrix where the array element index numbers p and q are both even.

5. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 1 is characterized in that: Determine the position vector of the array surface integral point, and calculate the position vector of all integral points on the entire array surface using homogeneous transformation based on the position vector of the array element center point and the relative position vector of the array element integral point relative to the center point.

6. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 1 is characterized in that: Determine the mode excitation coefficient matrix and mode coupling matrix of the folded array antenna under different folding conditions, including: According to the position vector of the obtained integral point, the coupling coefficients of each order mode of each element of the array antenna under different working conditions are obtained; Calculate the mode excitation coefficient based on the mode coupling coefficient; According to the mode coupling coefficient and the mode excitation coefficient, the mode excitation coefficient matrix and the mode coupling matrix are calculated.

7. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 6 is characterized in that: The calculation formula for the coupling coefficient of each order mode of each element of the array antenna under different working conditions is: Where: j is the imaginary unit, ω is the angular frequency of the electromagnetic wave, μ is the magnetic permeability of free space, S n 、S m denote the integration domains of array elements n and m respectively, The relationship between the a-order mode current of element m and the b-order mode current of element n is represented by r. d (τ,θ M ) is the position vector of the integral point on the m radiation unit on the folded array when the folding angle is θ, r d ′(τ,θ M ) is the position vector of the integral point on the n radiation unit on the folded array when the folding angle is θ, G(r d (τ,θ),r′ d (τ,θ)) is the Green function, are the a-order mode current of the m-th array element and the b-order mode current of the n-th array element, k is the free space wave number, is the Hamiltonian operator, is a two-dimensional Hamiltonian operator.

8. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 6 is characterized in that: The mode excitation coefficient is calculated based on the mode coupling coefficient: In the formula, j is the imaginary unit, N is the number of array elements, is the a-order mode excitation coefficient of array element m, is the a-order initial mode excitation coefficient of array element m, is the mode coupling coefficient under different working conditions, characterizing the mutual coupling effect of array elements n and m in modes a and b, λ b is the b-th order eigenvalue, is the mode coupling matrix of array element n to array element m in the a-order mode, Γ n Represents the excitation coefficient matrix of each order mode of array element n, Λ n is a diagonal matrix of eigenvalues of array element n.

9. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 6, characterized in that: The calculated mode excitation coefficient matrix and mode coupling matrix are: C=C 0 +GLC Miura Where Γ is the mode excitation coefficient matrix, Γ 0 is the array of initial mode excitation coefficients of each element of the array antenna, Λ is the diagonal matrix of the eigenvalues of each element of the array antenna, C Miura is the mode coupling matrix of the folded array.

10. The method for rapidly estimating the electrical performance of a large foldable array antenna under all working conditions according to claim 1, characterized in that: The far-field pattern E(θ,φ) of the folded array antenna under various working conditions is: Where j is the imaginary unit, ω is the angular frequency of the electromagnetic wave, μ is the magnetic permeability of free space, k is the wave number in free space, r is the distance from the observation point, and Γ 0 is the array of initial mode excitation coefficients of each element of the array antenna, U is the unit matrix, C Miura is the mode coupling matrix of the folded array, Λ is the diagonal matrix of the eigenvalues of each element of the array antenna, and F is the far-field pattern matrix of each antenna in the folded array antenna after the spatial phase term and antenna pointing change due to the change of antenna position.

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