Double-reflector antenna electromechanical coupling rapid analysis method and system

Abstract

The invention discloses a double-reflector antenna electromechanical coupling rapid analysis method and system, and aims to reconstruct a physical optical integral expression. Dispersing the reflecting surface into triangular grids, and performing linear fitting on amplitude and phase functions in each grid; an equivalent wave number / wavelength concept is introduced, a phase fitting error is analyzed, a differentiated grid processing strategy is put forward, a closed expression for calculating a far-field directional diagram is deduced through affine transformation and partial integration, and numerical integration is replaced by analytical calculation; and converting the structural deformation into an additional phase error, and integrating the additional phase error into a rapid calculation framework. The method breaks through the limitation of the traditional electromagnetic analysis on the grid size, greatly improves the electromechanical coupling analysis speed on the premise of guaranteeing the precision, and provides an efficient tool for the design and profile compensation of a high-frequency-band antenna.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of dual-reflector antennas, and relates to a dual-reflector antenna electromechanical coupling rapid analysis method and system. BACKGROUND

[0002] Reflector antennas are the core equipment in national major engineering tasks such as satellite communication, radar systems, weather observation and radio astronomy. With the rapid development of radio astronomy, deep space exploration and earth observation, the demand for large-aperture, high-frequency reflector antennas is increasing. The main development direction of this kind of antenna technology is large aperture and high frequency, aiming to meet the needs of scientific research and engineering application for higher sensitivity, higher resolution and wider frequency spectrum coverage. However, during service, factors such as manufacturing process, installation error and environmental load will cause deviations in the antenna structure, and thus cause the performance of the antenna to decline. Especially in large-aperture and high-frequency applications, the electromechanical coupling problem is more prominent, and higher requirements are put forward for the compensation technology of the antenna.

[0003] In the research and engineering application of reflector antennas, the physical optics method (PO) is one of the key methods for calculating the far-field pattern of the antenna. When calculating the electrical performance, the electromechanical coupling model of the antenna needs to be solved repeatedly. However, the complexity of the solution is closely related to the division of the electromagnetic grid. With the development of antennas towards large aperture and high frequency, in order to ensure the calculation accuracy, the electromagnetic analysis grid size used in the analysis of the traditional physical optics method is limited to λ / 5 to λ / 3, which leads to a sharp increase in the number of grids and brings a huge computational burden. In order to improve the solving efficiency, one of the research directions is to deeply analyze the factors that limit the size of the electromagnetic calculation unit, such as grid discretization error and oscillation properties of far-field integration, and to explore methods to relax the restrictions on the size of the unit, so as to realize the rapid solution of the model.

[0004] MATLAB is a high-level numerical analysis environment developed by MathWorks Company. The software provides powerful matrix operation capability, numerical calculation function library and programmable development framework, supports analytical processing of electromagnetic data, parameter optimization and visualization verification.

[0005] GRASP is a high-end commercial software for reflector antenna analysis and design developed by TICRA Company. The software takes the physical optics method (PO) combined with the physical diffraction theory (PTD) as the core algorithm, and integrates various efficient numerical methods such as the method of moments (MoM), which has the ability to analyze and optimize the radiation characteristics (such as far-field pattern, gain, cross-polarization) of complex antennas such as single / dual reflector antennas, shaped reflector antennas and array feeding systems with high precision and high efficiency. SUMMARY

[0006] In order to solve the problem that the solving complexity of the electromechanical coupling model is significantly improved with the increase of the antenna size and the increase of the working frequency, the application aims to provide a fast electromechanical coupling analysis method for a dual-reflector antenna, break through the limitation of the grid size in the traditional electromagnetic analysis, accelerate the solving speed, and more efficiently serve the design and compensation requirements of the dual-reflector antenna.

[0007] The application is realized by the following technical solutions: The application is realized by the following technical solutions: According to the geometric relationship and the coordinate transformation of the dual-reflector antenna, the physical optical integral expression for far field calculation is reconstructed. The antenna reflector is discretized into a plurality of structural grid units, and in each structural grid unit, the amplitude function and the phase function in the physical optical integral are linearly fitted. Based on the equivalent wave number and the equivalent wavelength, the phase fitting error introduced by the linear fitting in the two physical optical integrations is analyzed, and based on the relationship between the phase fitting error and different working wavelengths, a phase error coefficient is obtained. Based on the phase error coefficient, a differentiated processing strategy is adopted for the structural grids of the primary reflector and the secondary reflector. By performing affine transformation and partial integration in the integral region of the processed structural grids of the primary reflector and the secondary reflector, the physical optical integral after linear fitting is solved, and a closed expression of the ideal dual-reflector far field pattern is obtained. The grid node displacement caused by the antenna structure deformation is obtained, the additional phase error introduced by the structure deformation at the grid centroid is calculated, and based on the closed expression, the deformed far field pattern containing the additional phase error is solved, realizing the fast analysis of the electromechanical coupling of the dual-reflector antenna.

[0008] Preferably, according to the geometric relationship and the coordinate transformation of the dual-reflector antenna, the physical optical integral expression for far field calculation is reconstructed, specifically: According to the geometric relationship of the dual-reflector antenna, based on the conversion relationship between the spherical coordinate system and the rectangular coordinate system and the surface Jacobian transformation, the two physical optical integral expressions in the process of solving the far field of the antenna are transformed, and the two physical optical integral expressions are respectively the first integral expression for solving the magnetic field of the primary reflector from the current of the secondary reflector and the second integral expression extracted from the primary reflector current for solving the far field expression. The dual-reflector antenna is a Gregorian dual-reflector antenna, the primary reflector is a parabolic surface, and the secondary reflector is an ellipsoidal surface.

[0009] Preferably, the reconstructed physical optical integral expression for far field calculation is:

[0010] The first integral expression for solving the main reflector magnetic field from the sub-reflector current is: ; Wherein, ; ; In the formula, is a unit vector, denotes a unit vector along the electromagnetic wave propagation direction; denotes a vector; is the magnetic field generated at a point on the main reflector; is a point on the main reflector, is a sub-reflector, is the distance from a point on the sub-reflector to the feed, ; is the wave number, denoted as: ; , is the distance from a point on the main reflector to a point on the sub-reflector, is the unit direction vector of ; Amplitude function on the sub-reflector; is the rectangular coordinate of a point on the main reflector, is the rectangular coordinate of the feed, is the length of the major axis of the ellipsoidal surface, is the length of the minor axis of the ellipsoidal surface; The second integral expression for solving the far field from the main reflector current is: ; In the formula, is defined as the core integral term of the far field expression; is the spherical coordinate angle of the far field observation direction, is the observation angle, is the azimuth angle, is the amplitude function on the main reflector; Rectangular coordinates of a point on the main reflector; ; ; is the main reflector, is the focal length of the main reflector.

[0011] Preferably, the amplitude function and the phase function in the physical optics integral are linearly fitted, specifically: The main reflector and the sub-reflector of the antenna are discretized into multiple triangular structure grids using triangular shell elements, and the amplitude function and the phase function in the two physical optics integral processes are linearly fitted in each triangular grid, wherein, Amplitude function on the primary reflector surface The linear fit expression is: ; Amplitude function on the secondary reflector surface The linear fit expression is:

[0012] wherein, is the coefficient of the linear fit on the primary reflector surface; , , is the coefficient of the linear fit on the secondary reflector surface; Phase function on the primary reflector surface The linear fit expression is: ; wherein, is the coefficient of the linear fit on the primary reflector surface; is the observation angle, is the azimuth angle; is the focal length of the primary reflector surface; ; is the wave number, expressed as: ; Based on the linear fit expression of the phase function on the primary reflector surface, a first fit error is obtained e m is defined as:

[0013] wherein, is the coefficient of the linear fit on the primary reflector surface; Phase function on the secondary reflector surface The linear fit expression is:

[0014] Based on the linear fit expression of the phase function on the secondary reflector surface, a second fit error is obtained e s is defined as: ; wherein, , , is the coefficient of the linear fit on the secondary reflector surface.

[0015] Preferably, based on the equivalent wave number and the equivalent wavelength, the phase fit error introduced by the linear fit in the two physical optical integrations is analyzed, specifically: In the region of the main lobe and the adjacent side lobe, define the equivalent wave number of the second integral expression for solving the far field from the main reflector current as: The corresponding equivalent wavelength is: , In the formula, is the observation angle coefficient related to the number of side lobes, is the diameter of the main reflector in the double reflector almost maintains a constant; Calculate the first fitting error caused by linear fitting of the phase function of the second integral expression , and define the first phase error coefficient as , and the first fitting phase error is ; Calculate the second fitting error caused by linear fitting of the phase function of the first integral expression for solving the main reflector magnetic field from the secondary reflector current , and define the second phase error coefficient as , and the second fitting phase error is ; Based on the second fitting phase error, the influence of the secondary reflector fitting phase error on the main reflector magnetic field is: ; Based on the first fitting phase error, the influence of the main reflector fitting phase error on the core integral term is expressed as: ; Based on the relationship between the phase fitting error and different operating wavelengths, when the operating wavelength is in the high frequency band, the first phase error coefficient is independent of frequency, and the second phase error coefficient increases with the increase of frequency.

[0016] Preferably, a differentiated processing strategy is adopted, specifically: Keep the grid division of the main reflector unchanged, and adaptively refine the grid of the secondary reflector according to the second phase error coefficient, specifically: When the second phase error coefficient is greater than a preset threshold, the triangular grid is refined; wherein the refinement includes reducing the side length of the triangular grid to one third of the original side length; wherein the preset threshold is 0.02.

[0017] Preferably, affine transformation and partial integration are performed in the integral region of the processed main reflector and secondary reflector structure grid, specifically: The first integral expression in any structure grid unit is: ; through affine transformation ; transforming any of its structural grid cells into a standard integration interval: ; the second integration expression after affine transformation is: ; wherein, ; wherein: is the integration result on the standard structural grid cell region derived through the method of integration by parts, which is a complex number; is the linear fitting coefficient of the amplitude function within the structural grid cell, is the linear fitting coefficient of the phase function within the grid cell, is the linear fitting coefficient of the phase function after combining like terms within the grid cell; is the affine transformation coefficient for mapping any grid cell to a standard grid cell, is the focal length of the main reflector, is a real constant related to the linear fitting coefficients of the structural grid cell and the affine transformation; is the equivalent wave number; substitute the linearly fitted amplitude function and phase function into the second integration expression after affine transformation; perform integration by parts on the substituted second integration expression within the standard integration interval to obtain a closed-form analytical expression of the far-field contribution of the structural grid cell; based on the closed-form analytical expression of the far-field contribution of the structural grid cell, vectorially superimpose the far-field contributions of all structural grid cells to obtain a closed-form expression of the ideal dual-reflector far-field pattern.

[0018] Preferably, the closed-form analytical expression of the far-field contribution of the structural grid cell is obtained by solving the second integration expression within the standard integration interval through integration by parts: .

[0019] Preferably, the grid node displacement caused by antenna structure deformation is obtained, and the additional phase error introduced by the structural deformation at the grid centroid is calculated, specifically: obtain the z-direction deformation of each vertex of the triangular grid in the structural grid of the main reflector and the sub-reflector obtained through finite element analysis; calculate the z-direction deformation at the centroid of each triangular grid through vertex interpolation ; calculate the additional phase error introduced by the z-direction deformation at the i-th grid centroid whose expression is: wherein is the opening angle at the grid centroid; the additional phase error is multiplied into the closed expression of the ideal dual-reflector far-field pattern as a phase factor , to obtain the deformed far-field contribution of the grid, and the deformed far-field contribution of the i-th grid is

[0020] The far-field pattern of the deformed reflector antenna is obtained by summing up the deformed far-field contributions of all the grids.

[0021] A fast electromechanical coupling analysis system for a dual-reflector antenna, comprising: a reconstruction module configured to reconstruct a physical optics integral expression for far-field calculation according to geometric relationships and coordinate transformation of the dual-reflector antenna; a linear fitting module configured to discretize the reflector of the antenna into a plurality of structural grid units, and perform linear fitting on amplitude functions and phase functions in the physical optics integral in each structural grid unit; a phase error coefficient acquisition module configured to analyze phase fitting errors introduced by the linear fitting in two physical optics integrals based on equivalent wave numbers and equivalent wavelengths, and obtain phase error coefficients based on relationships between the phase fitting errors and different operating wavelengths; a processing strategy design module configured to adopt differentiated processing strategies for structural grids of the primary reflector and the secondary reflector based on the phase error coefficients; a closed expression acquisition module configured to perform affine transformation and partial integration in integral regions of the processed structural grids of the primary reflector and the secondary reflector, solve the linearly fitted physical optics integral, and obtain a closed expression of an ideal dual-reflector far-field pattern; a far-field pattern acquisition module configured to acquire grid node displacements caused by structural deformation of the antenna, calculate additional phase errors introduced by the structural deformation at grid centroids, and solve a deformed far-field pattern containing the additional phase errors based on the closed expression, to realize fast electromechanical coupling analysis of the dual-reflector antenna.

[0022] Compared with the prior art, the present application has the following beneficial technical effects: ​The application discloses a kind of dual-reflector antenna electromechanical coupling fast analysis method and system, to solve the problem of low computational efficiency caused by grid over-dense in the analysis of large high-frequency reflector antenna.The differentiated grid processing strategy is proposed: the main reflector grid is fixed unchanged, and the grid of the secondary reflector is refined adaptively according to the error coefficient.This strategy breaks through the rigid restriction that the grid size must change with frequency in traditional electromagnetic analysis, and avoids the unnecessary encryption of the main reflector grid in the high-frequency band, significantly reducing the total grid number.Meanwhile, by introducing the concept of equivalent wavelength, the phase error coefficient is quantitatively defined, providing a clear accuracy criterion for linear fitting and grid division.Especially for the secondary reflector, which is the main source of error, a phase error coefficient threshold is set as the trigger condition for adaptive grid refinement.This closed-loop control mechanism based on strict error analysis ensures that the calculation accuracy meets the engineering design requirements at any frequency, making the results of the fast analysis method reliable and confident.The structural deformation is converted into additional phase error and integrated into the fast calculation framework.The application breaks through the limitation of grid size in traditional electromagnetic analysis, greatly improves the electromechanical coupling analysis speed under the premise of ensuring accuracy, and provides an efficient tool for high-frequency antenna design and surface compensation.The application simplifies the electromechanical coupling analysis process of reflector antenna, realizes efficient calculation of antenna electrical performance under different working frequencies without refining the structure grid or increasing the number of integration points, and ensures high calculation accuracy.The application provides a practical and efficient solution for electromechanical coupling analysis of high-frequency reflector antennas, which helps to shorten the antenna design cycle and has important engineering application value.

[0023] Further, the method efficiently maps the influence of structural deformation into additional phase error and directly embeds it into the fast electromagnetic calculation framework.This enables engineers to quickly evaluate the electrical performance changes under multiple load conditions (such as gravity, temperature) after a single structural finite element analysis.This process closely follows engineering practice, providing a powerful fast simulation tool for antenna surface optimization, material selection in the design stage, and real-time surface compensation in the use stage, which can support high-frequency design iteration, significantly shorten the antenna development cycle, and reduce development cost and risk. BRIEF DESCRIPTION OF DRAWINGS

[0024] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed to be used in the embodiments, it should be understood that the following drawings only show some embodiments of the application, therefore should not be regarded as a limitation to the scope, for those skilled in the art, without creative labor, other related drawings can also be obtained from these drawings.

[0025] Figure 1 The method flowchart of the application; Figure 2 A schematic diagram of a dual-reflector antenna in the present application; Figure 3 A schematic diagram of equivalent wavelength varying with frequency in the present application; Figure 4 A schematic diagram of phase error coefficient varying with frequency in the present application; Figure 5 A schematic diagram of comparison before and after the grid refinement of the sub-reflector in the present application; Figure 6 A comparison diagram of ideal antenna far-field patterns obtained by using the proposed method and GRASP at frequencies of 100 GHz and 500 GHz in the present application; Figure 7 A comparison diagram of deformed antenna far-field patterns obtained by using the proposed method and GRASP at frequencies of 100 GHz and 500 GHz in the present application; Figure 8 A comparison diagram of calculation time of the proposed method and GRASP at frequencies of 100 GHz to 500 GHz in the present application. DETAILED DESCRIPTION

[0026] In order to make the purpose, technical scheme and advantages of the embodiments of the present application clearer, the technical scheme in the embodiments of the present application will be described clearly and completely below in conjunction with the drawings in the embodiments of the present application. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. The components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present application provided in the drawings is not intended to limit the scope of the claimed present application, but only represents selected embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by those of ordinary skill in the art without creative labor fall within the scope of protection of the present application.

[0027] The present application provides a dual-reflector antenna electromechanical coupling fast analysis method, aiming to solve the problem of huge calculation amount of large high-frequency antenna electromechanical coupling analysis. The core principle is to introduce the concept of equivalent wavelength, reveal the different dependence of phase fitting error on working frequency of the main and sub reflectors, propose the strategy of fixed grid of the main reflector and adaptive grid of the sub reflector, and finally realize the leap of analysis speed by deducing the integral closed expression instead of numerical integration. The embodiments of the present application will be described in detail below in conjunction with a Gregorian dual-reflector antenna.

[0028] Figure 1 A flowchart of the dual-reflector antenna electromechanical coupling fast analysis method of the present application. As shown in Figure 1 the present application method includes the following steps: Step S1: Based on the geometric relationship and coordinate transformation of the dual-reflector antenna, reconstruct the physical optical integral expression for far-field calculation; specifically: Based on the geometric relationship of the dual-reflector antenna, the two physical optical integral expressions in the antenna far-field solution process are transformed according to the transformation relationship between spherical coordinates and rectangular coordinates and the surface Jacobian transformation. The initial physical optics integral expression is: ; In the formula,

[0029]

[0030] In the formula, As a unit dyadic vector, its mathematical expression in spherical coordinates is: Its mathematical property is that any vector multiplied by the unit vector will result in the vector itself. Represents a unit vector along the direction of electromagnetic wave propagation (radial); The term dyadic vector is used in calculations to project any vector onto the radial direction. From source vector The direction of its dissemination was subtracted from the middle. The component on the upper part (i.e., the radial component) is retained, thus preserving the lateral component perpendicular to the direction of propagation; ; The two physical optical integral expressions are respectively the first integral expression for solving the magnetic field of the main reflector from the sub-reflector current and the second integral expression for solving the far field from the main reflector current; The dual-reflector antenna is a Gregorian dual-reflector antenna, with its main reflector being a parabolic surface and its secondary reflector being an ellipsoidal surface. This step is fundamental to all subsequent accelerated processing. First, it's established that the object of analysis is a Gregorian dual-reflector antenna, with its primary reflector (referred to as the primary reflector) being a paraboloid of revolution and its secondary reflector (referred to as the secondary reflector) being an ellipsoid of revolution. [Antenna far-field radiation pattern] The solution is obtained using standard two physical optical integrals: The two physical optics integral expressions are respectively the second integral expression for solving the far field from the current of the primary reflector and the first integral expression for solving the magnetic field of the primary reflector from the current of the secondary reflector. 1. First integration (solving the first integral expression of the magnetic field of the main reflector from the current of the secondary reflector): Calculate the magnetic field generated by the current induced on the secondary reflector by the feed source, and the magnetic field on the main reflector. value at point The expression is:

[0031] where, is the magnetic field produced at a point on the main reflector surface; is the imaginary unit, , is the wave number (k = 2π / λ), is the operating wavelength, is the sub-reflector surface, is a point on the sub-reflector surface, is the sub-reflector surface induced current, is the distance from the main reflector surface observation point to the sub-reflector surface point , is the unit vector in the direction, ; 2. Second integration (second integral expression for solving the far field from the main reflector surface current): the current on the main reflector surface is taken as the source to calculate the far field radiation . The core is to calculate the radiation vector :

[0032] where, is the main reflector surface, is the observation angle, is the azimuth angle, is the unit normal vector of the main reflector surface, is the unit vector of the far field observation direction, is the free space wave impedance, is the far field observation distance.

[0033] In order to facilitate subsequent discretization and linear fitting, the above integral must be geometrically reconstructed. By using the geometric relationship of the main reflector parabola (focal length ), the sub-reflector ellipsoid equation, and the conversion relationship between the rectangular coordinate system and the spherical coordinate system, and introducing the surface Jacobian transformation, the expression is: Convert the area element to the projection plane element , and the second integral expression and the first integral expression physical optics integral expression can be reconstructed as the integral on the aperture plane in the rectangular coordinate system: The reconstructed integral formula for solving the main reflector surface magnetic field from the sub-reflector surface current is: ; where, is the amplitude function on the sub-reflector surface.

[0034] The reconstructed main reflector surface current solving far-field integral formula is:

[0035] wherein, is the amplitude function on the main reflector surface, which contains the comprehensive vector of the normal of the main reflector surface, magnetic field and other information.

[0036] wherein, In the formula, is the rectangular coordinate of the observation point on the main reflector surface, is the rectangular coordinate of the phase center of the feed source. The height of the point on the sub-reflector surface is constrained by the ellipsoid equation:

[0037] In the formula, and are ellipsoid coefficients, which determine the aperture and depth of the sub-reflector.

[0038] Step S2: discretize the antenna reflector into a plurality of structural grid cells, and in each structural grid cell, linearly fit the amplitude function and the phase function in the physical optical integral, specifically: discretize the main reflector and the sub-reflector of the antenna into a plurality of triangular structural grids using triangular shell elements, and in each triangular grid, linearly fit the amplitude function and the phase function in the two physical optical integral processes, This step aims to convert the continuous integral problem into a piecewise summation problem and create conditions for subsequent derivation of a closed solution.

[0039] 1. Surface discretization: triangular shell elements are used to divide the main reflector and the sub-reflector into grids. These grids are both structural analysis units and electromagnetic integral units, realizing the unification of mechanical and electrical data.

[0040] Amplitude function linear fitting: in each triangular element, the amplitude function and is considered to change smoothly and can be approximated by a first-degree polynomial (plane):

[0041]

[0042] In the formula, is the linear fitting coefficient (vector) obtained by fitting the vertex values of the element.

[0043] Phase function linear fitting: ​The phase function of the reconstructed primary reflector current solving far-field integral formula is nonlinear. In each triangular element, the whole is directly linearly fitted: It contains quadratic terms by itself. In each triangular element, only the quadratic term part caused by the curved surface is linearly fitted , and the expression is:

[0044] The first phase fitting error is denoted as . The fitted is completely linear in the element.

[0045] The first phase fitting error e m is defined as:

[0046] The phase function of the reconstructed secondary reflector current solving primary reflector magnetic field integral formula is nonlinear. In each triangular element, the whole is directly linearly fitted:

[0047] The second phase fitting error is denoted as ; in which is the fitting coefficient.

[0048] The second phase fitting error e s is defined as:

[0049] Through this step, the original integral is transformed into a form in which the integral function is a linear polynomial multiplied by an exponential linear phase in each triangular element, which is a key prerequisite for obtaining a closed solution.

[0050] Step S3: Based on the equivalent wave number and the equivalent wavelength, analyze the phase fitting error introduced by the linear fitting in the two physical optics integrations; and based on the relationship between the phase fitting error and different operating wavelengths, obtain a phase error coefficient; The purpose of this step is to quantitatively evaluate the error introduced by the linear fitting, and to reveal the relationship between the error and the frequency, so as to guide the grid division strategy.

[0051] Reconstructed primary reflector current solving far-field integral phase error analysis: In the main lobe and adjacent side lobe regions (i.e. smaller), small-angle approximation ( ) is performed, and it can be found that the first term in dominates. It can be approximately expressed as: ​

[0052] where k is the equivalent wave number. Considering the maximum observation angle:

[0053] where k is the equivalent wave number. Considering the maximum observation angle: is the observation angle coefficient related to the number of side lobes, which directly affects the number of side lobes in the observed pattern. At high frequencies, increases but decreases, making tend to a stable value at high frequencies, so also tends to be stable. is the diameter of the main reflector in the dual-reflector. As the frequency increases, the wave number increases, and the change trend of the two parts in the formula is opposite. At high frequencies, the increase and decrease of the two parts cancel each other out, almost maintaining a constant.

[0054] For the equivalent wave number, the equivalent wavelength is defined.

[0055] When linear fitting the phase function inside the main reflector structure grid, the first phase error brought by it is:

[0056] The first phase error coefficient is defined as:

[0057] The first fitting phase error is ; Since is stable at high frequencies, and is related to the cell size but not the frequency, therefore is basically independent of the operating frequency at high frequencies.

[0058] The reconstructed main reflector magnetic field integral from the secondary reflector current: The secondary reflector performs linear fitting on the phase function inside the secondary reflector structure grid, and the phase error brought by it is:

[0059] The second phase error coefficient is defined as: where is the actual operating wavelength. Since is determined by the cell size, when the frequency increases ( decreases), the will significantly increase.

[0060] The second fitting phase error is ; Step S4: Adopting differentiated processing strategies for the structure grids of the main reflector and the secondary reflector based on the phase error coefficients;​ Based on the deep analysis of step S3, the present application proposes a differentiated mesh processing strategy: Primary reflector mesh: Since is independent of frequency, the structured mesh for primary reflector surface integration does not need to be refined with frequency. A set of mesh designed and verified at low frequency can be applied to all high frequency calculations.

[0061] Secondary reflector mesh: Since increases with frequency, to ensure calculation accuracy, the secondary reflector mesh must be adaptively refined.

[0062] Refinement criterion: Set a phase error coefficient threshold, for example When the calculated exceeds this threshold, the secondary reflector triangular mesh is refined.

[0063] Refinement method: Use mesh subdivision, for example, connect the midpoint of each triangular edge to subdivide a triangle into four similar small triangles, at this time the new mesh edge length is about one third of the original edge length. Repeat this process until the of all elements meets the requirements.

[0064] This strategy is one of the cores of the method to achieve rapidity, it breaks the traditional thinking that the mesh must be globally refined to meet high frequency accuracy, only the secondary reflector with large error contribution is refined, greatly reducing the total number of meshes.

[0065] Step S5: Solve the linearly fitted physical optical integral by affine transformation and partial integration in the integration region of the processed primary reflector and secondary reflector structured mesh, obtain the closed expression of the ideal dual reflector far field pattern; This step solves the far field integral formula for the primary reflector current after linear fitting, derives the closed solution of the integral on each structured mesh element, completely avoids numerical integration.

[0066] When calculating the integral , consider the first structured mesh element, substitute the fitted amplitude function (9) and linearized phase function, the integral in any structured mesh is:

[0067] According to affine transformation, map any structured mesh element to a standard right triangle (vertices (0, 0), (1, 0), (0, 1)) on the parameter plane : Transform any structured mesh into a standard integration interval:

[0068] The integral becomes:

[0069] where,

[0070] According to the partial integral, the closed-form analytic expressions of the form can be obtained, which are explicit functions of the transformation coefficients and the equivalent wave number , the azimuth angle . The closed-form expression of the far-field pattern of the ideal dual-reflector:

[0071] where is a constant determined by the transformation coefficients and the angles. can be finally expressed as a linear combination of .

[0072] Pattern synthesis: the far-field contributions of all the triangular elements of the antenna are calculated and vectorially superimposed. Finally, the far-field contributions of all the meshes are superimposed, and the far-field pattern of the deformed reflector antenna is obtained.

[0073] This step is a purely analytical calculation, and its calculation time is much less than that of numerical integration, and the calculation amount is only linearly related to the number of meshes and is independent of the frequency.

[0074] Step S6: Obtain the displacement of the mesh nodes caused by the deformation of the antenna structure, calculate the additional phase error introduced by the deformation of the structure at the centroid of the mesh, and solve the deformed far-field pattern containing the additional phase error based on the closed-form expression, to realize the fast analysis of the electromechanical coupling of the dual-reflector antenna.

[0075] This step embeds the influence of mechanical deformation into the above fast electromagnetic calculation framework in the form of phase error.

[0076] Obtain the structure deformation data: through the finite element analysis software (such as ANSYS), the mechanical and thermal analysis of the antenna structure is carried out, and the displacement of each structure mesh node is obtained, especially the z-direction deformation .

[0077] Calculate the centroid deformation of the unit: for each triangular element, the z-direction deformation at the centroid of the element is calculated by linear interpolation using the deformation of its three vertices .

[0078] Introduce the deformation additional phase error: the deformation of the structure causes the position of the reflector to deviate from the ideal position, thereby introducing an additional phase error. For the jth mesh, the additional phase error is For each grid, the additional phase error can be approximated as:

[0079] In the formula, The deformation of the mesh centroid. The angle subtended by the centroid of the grid. The cosine term reflects the relationship between the deformation direction and the observation direction.

[0080] Calculate the deformed far field: As an additional phase factor, multiplied into step S5, the deformation far-field contribution within the i-th grid is obtained as follows: ; Then, all the grids Vector superposition yields the far-field radiation pattern of the deformed antenna.

[0081] Thus, this invention completes a comprehensive electromechanical coupling rapid analysis process, from ideal antenna modeling, error analysis, fast algorithm design to structural deformation integration. Through the above steps, this invention has the following significant advantages when analyzing large high-frequency dual-reflector antennas: extremely fast computation speed: the computational complexity based on closed expressions is far lower than that of traditional numerical integration, and the fixed mesh of the main reflector reduces the total number of meshes at high frequencies; controllable accuracy: the adaptive mesh strategy based on rigorous error analysis ensures computational accuracy; strong engineering practicality: the process is clear and easy to integrate with existing structural analysis tools (such as ANSYS), providing an efficient analysis method for antenna optimization design and surface compensation.

[0082] A rapid analysis system for electromechanical coupling of a dual-reflector antenna, characterized in that it comprises: The reconstruction module reconstructs the physical optical integral expression for far-field calculation based on the geometric relationship and coordinate transformation of the dual-reflector antenna. The linear fitting module discretizes the antenna reflector into multiple structural grid cells, and performs linear fitting on the amplitude function and phase function in the physical optical integral within each structural grid cell; The phase error coefficient acquisition module analyzes the phase fitting error introduced by the linear fitting in two physical optical integrations based on the equivalent wavenumber and equivalent wavelength; and obtains the phase error coefficient based on the relationship between the phase fitting error and different working wavelengths. The processing strategy design module adopts differentiated processing strategies for the structural mesh of the main reflector and the sub-reflector based on the phase error coefficient; The closed-form expression acquisition module obtains the closed-form expression of the far-field radiation pattern of the ideal dual-reflector by performing affine transformation and integration by parts in the integration region within the structured grid of the processed primary and secondary reflectors, solving the physical optics integral after linear fitting; The far field pattern acquisition module acquires the grid node displacement caused by the deformation of the antenna structure, calculates the additional phase error introduced by the deformation of the structure at the grid centroid, and solves the deformed far field pattern containing the additional phase error based on the closed expression, so as to realize the fast analysis of the electromechanical coupling of the dual-reflector antenna.

[0083] The technical solutions of the present application will be described clearly and completely below. Obviously, the described embodiments are part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0084] Embodiment 1 As shown in Figure 1 A fast analysis method of electromechanical coupling of a dual-reflector antenna, which comprises the following sequential steps: (1) According to the geometric relationship of the dual-reflector antenna, the conversion relationship between the spherical coordinate system and the rectangular coordinate system, and the expression of the two physical optical integrations in the process of solving the far field of the antenna, the transformation is carried out. The two physical optical integrations are the solving process of the main reflector magnetic field from the sub-reflector current and the solving process of the far field from the main reflector current.

[0085] (2) Discretize the antenna surface into a plurality of structural grid elements. In each element, a linear fitting is performed on the amplitude function and the phase function using a polynomial.

[0086] (3) According to the established concepts of equivalent wave number and equivalent wavelength, the influence of the linear fitting error of the phase function in the solving process of the two physical optical integrations on the far field pattern is analyzed.

[0087] (4) According to the relationship between different working wavelengths and the linear fitting error, different processing methods are adopted for the main reflector and the sub-reflector structural grid.

[0088] (5) According to the affine transformation of the integral region and the partial integration, a closed expression for calculating the far field pattern of the ideal dual-reflector antenna is obtained.

[0089] (6) According to the deformation amount of the structural grid nodes, the deformation amount of the integral grid centroid is calculated, and finally the fast analysis method of electromechanical coupling of the dual-reflector antenna is obtained according to the phase error caused by the structural deformation.

[0090] The step (1) is specifically referred to as Figure 2As shown, the analyzed dual-reflector antenna is a Gregorian dual-reflector antenna, with a parabolic primary reflector and an ellipsoidal secondary reflector. The diameter of the primary reflector is 2.2m, the diameter of the secondary reflector is 0.22m, the focal length of the primary reflector is 0.66m, the focal length of the secondary reflector is 0.594m, and the eccentricity of the secondary reflector is 0.8073.

[0091] The physical optics integral expression is:

[0092] in,

[0093]

[0094] In the formula, These are the primary reflecting surface and the ellipsoidal secondary reflecting surface, respectively. At a point on the main reflective surface, The unit normal vector of a point on the main reflecting surface. The magnetic field at a point on the main reflecting surface. For a point on the sub-reflector surface, for arrive distance, for The unit direction vector.

[0095] The geometric relationship of the dual-reflector antenna is as follows: ; ;

[0096] In the formula, Focal length of the main reflecting surface A point on the main reflecting surface in spherical coordinates Towards the component.

[0097] The surface Jacobian transformation formula is:

[0098] Based on the antenna geometry, surface Jacobian transformation, and coordinate system transformations, the physical optics integral expression is transformed into an integral on the aperture plane in Cartesian coordinates:

[0099]

[0100] in,

[0101]

[0102] wherein, is the rectangular coordinate of a point on the main reflector, is the rectangular coordinate of the feed, is the ellipsoid coefficient, is the coefficient of linear fitting.

[0103] The step (2) is specifically referring to: as shown in the figure, using triangular shell elements to discretize the main reflector and the sub-reflector of the antenna. The edge length of the main reflector grid element is 5 cm, and the edge length of the sub-reflector structure grid is 1 cm. Figure 3

[0104] The amplitude function in the twice integral process is linearly approximated using the following first-order polynomial:

[0105]

[0106] wherein, is the coefficient of linear fitting.

[0107] When calculating the integral , the phase function part itself is in the form of a quadratic polynomial, and the quadratic term part in the polynomial is linearly fitted:

[0108] The first fitting error is defined as:

[0109] When calculating the integral , the linear fitting is performed on :

[0110] The second fitting error is defined as:

[0111] The step (3) is specifically referring to: when calculating the far-field pattern of the reflector antenna, only the main lobe and the adjacent side lobe need to be considered. In this area, approaches to , approaches to , thus when calculating the integral , , the first-order term is dominant, and can be approximately expressed as: ​

[0112] In the formula, This is called the equivalent wavenumber. Considering the maximum observation angle:

[0113] In the formula, This is the observation angle factor, which directly affects the number of sidelobes in the observed radiation pattern. In this example, By taking a value of approximately 380, the far-field pattern containing the main lobe and two side lobes on each side can be calculated.

[0114] As the frequency increases, the wavenumber increases, and the two parts in the formula... and The trends of change are opposite. For example... Figure 4 As shown, in the high-frequency range, the increases and decreases of the two cancel each other out. It remains almost constant. For the equivalent wavenumber, the equivalent wavelength is defined. In the high-frequency band, Similarly, maintain a constant value.

[0115] The first fitting error resulting from linear fitting within the main surface structure mesh is:

[0116] The first phase error coefficient of the principal plane is defined as:

[0117] The first phase error of the fit is defined as:

[0118] The second fitting error resulting from linear fitting within the sub-face structure mesh is:

[0119] The second phase error coefficient of the subplane is:

[0120] The second fitting phase error is defined as:

[0121] The effect of the second fitting phase error of the secondary surface on the magnetic field of the principal surface is as follows:

[0122] The effect of the principal plane fitting phase error on the antenna far-field radiation pattern is expressed as follows:

[0123] In the electrical performance calculation of a dual-reflector antenna, the fitting error introduced when linearly fitting the mesh of the main and secondary surfaces can be physically equivalent to the geometric deformation of the reflector surfaces.

[0124] This surface bias caused by model simplification (e.g. linear fitting) will change the reflection or propagation path length of electromagnetic wave on the surface of the structure, and then produce phase error. In this paper, the corresponding phase error coefficient and phase error are also defined to quantify this effect.

[0125] These phase errors caused by linear fitting will eventually deteriorate the antenna electrical performance, such as gain reduction, side lobe level lifting, etc. Therefore, it is necessary to judge the relationship between the fitting error and the (equivalent) wavelength according to the phase error coefficient, and then judge the influence degree of the fitting error on the far-field pattern.

[0126] The process of calculating the integral The phase error coefficient is basically independent of frequency at high frequency, and remains below , as shown by the curve Figure 4 in ; while calculating the integral , the phase error coefficient continuously increases with the increase of frequency, as shown by the curve Figure 4 in , which means that the error brought by linear fitting error to the far-field pattern also continuously increases with the increase of frequency.

[0127] The step (4) specifically refers to: since the main surface phase error coefficient is basically independent of frequency at high frequency, and remains below , so for the main surface structure grid, there is no need to change with the change of frequency, and it can remain unchanged when calculating the far-field pattern at different frequency bands; while for the secondary surface phase error coefficient , it continuously increases with the increase of frequency, so for the secondary surface structure grid, it is necessary to refine the secondary surface structure grid according to the change of the phase error coefficient . When the phase error coefficient is greater than 0.02, the triangular grid is refined once.

[0128] In this example, when the working frequency reaches 200GHz, the calculated phase error coefficient is greater than 0.02, and the triangular grid is refined once, and the grid length after refinement is one third of the original grid length. After grid refinement, the grid size is reduced and the number is increased, as shown in Figure 5 , which shows the comparison before and after the secondary surface grid refinement. At this time, the phase error coefficient is calculated again, and the refined phase error coefficient is less than 0.02 within the considered frequency band, as shown by the curve Figure 4 in .

[0129] The step (5) is specifically referring to: calculating integral The integral in the arbitrary structure grid is:

[0130] According to the affine transformation, the arbitrary structure grid is transformed into a standard integral interval:

[0131] The integral becomes:

[0132] In the formula,

[0133] According to the integral by parts, the closed expression of the integral is solved: ; In the formula: In the formula: The integral result on the standard structure grid unit area derived by the integral by parts is a complex number; is the linear fitting coefficient of the amplitude function in the structure grid unit, is the linear fitting coefficient of the phase function in the structure grid unit, is the linear fitting coefficient of the phase function after the same items are combined in the grid unit; is the affine transformation coefficient for mapping the arbitrary grid unit to the standard grid unit, is the focal length of the main reflecting surface, is a real constant related to the linear fitting coefficient of the structure grid unit and the affine transformation; is the equivalent wave number; At this time, the closed form of the calculation formula of the far field pattern of the ideal reflecting surface antenna can be obtained.

[0134] The step (5) is specifically referring to: the structure grid node deformation is obtained by the ANSYS finite element simulation software, the used structure grid is a triangular element, and the node deformation is the z-direction deformation of each triangular element three vertices. The z-direction deformation of the centroid in the element is obtained by the interpolation method, and the phase error in the i-th element due to the structure deformation can be expressed as:

[0135] In the formula, is the deformation of the grid centroid, is the opening angle of the grid centroid.

[0136] At this time, the deformed far field contribution in the i-th grid is:

[0137] Finally, the far-field contributions of all the meshes are superimposed to obtain the far-field pattern of the deformed reflector antenna.

[0138] To verify the effectiveness and efficiency of the method, the results of the method are compared with those of the commercial software GRASP.

[0139] As shown in Figs. Figure 6 Figs.

[0140] As shown in Figs. Figure 7 Figs.

[0141] As shown in Figs. Figure 8 Figs.

[0142] Figs. Figure 6 , Figure 7 , Figure 8 The results show that the method has high precision comparable to that of the commercial software GRASP, and greatly improves the calculation efficiency, especially in the terahertz frequency range, and solves the problem of heavy calculation burden in the background art.

[0143] In summary, the method simplifies the process of electromechanical coupling analysis of reflector antennas, realizes efficient calculation of high-frequency antenna electrical performance with only the need to refine the secondary surface mesh, keeps the calculation time basically unchanged, and guarantees high calculation precision.

[0144] The above merely describes preferred embodiments of the present application, and is not intended to limit the present application in any form; any person skilled in the art can easily implement the present application according to the drawings and the above description; however, any person skilled in the art can make some changes, modifications and equivalent changes within the scope of the technical solutions of the present application, and the equivalent embodiments of the present application are still within the protection scope of the technical solutions of the present application.

Claims

1. A rapid analysis method for electromechanical coupling of a dual-reflector antenna, characterized in that, include: Based on the geometric relationship and coordinate transformation of the dual-reflector antenna, the physical optical integral expression for far-field calculation is reconstructed; The antenna reflector is discretized into multiple structural grid cells, and within each structural grid cell, the amplitude function and phase function in the physical optical integral are linearly fitted. Based on the equivalent wavenumber and equivalent wavelength, the phase fitting error introduced by the linear fitting in two physical optical integrations is analyzed; and based on the relationship between the phase fitting error and different working wavelengths, the phase error coefficient is obtained. Different processing strategies are adopted for the structural mesh of the main reflector and the sub-reflector based on the phase error coefficient; By performing affine transformation and integration by parts within the integral region of the structured grid of the processed primary and secondary reflective surfaces, the physical optics integral after linear fitting is solved to obtain the closed expression of the far-field radiation pattern of the ideal dual reflective surfaces. The displacement of grid nodes caused by antenna structural deformation is obtained, the additional phase error introduced by structural deformation at the centroid of the grid is calculated, and the deformation far-field pattern containing the additional phase error is solved based on the closed expression, so as to realize the rapid electromechanical coupling analysis of dual reflector antenna.

2. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 1, characterized in that, Based on the geometric relationship and coordinate transformation of the dual-reflector antenna, the physical optical integral expression for far-field calculation is reconstructed as follows: Based on the geometric relationship of the dual-reflector antenna, the two physical optical integral expressions in the antenna far-field solution process are transformed according to the transformation relationship between spherical coordinate system and rectangular coordinate system and the surface Jacobian transformation. The two physical optical integral expressions are the first integral expression for solving the magnetic field of the main reflector from the sub-reflector current and the second integral expression extracted from the far-field expression for solving the main reflector current. The dual-reflector antenna is a Gregorian dual-reflector antenna, with its primary reflector being a parabola and its secondary reflector being an ellipsoid.

3. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 2, characterized in that, The physical optical integral expression for the reconstructed far-field calculation is as follows: The first integral expression for solving the magnetic field of the main reflecting surface from the current of the secondary reflecting surface is: ； in, ; ； In the formula, For unit vector, Represents a unit vector along the direction of electromagnetic wave propagation; Indicates parallel arrow; For a point on the primary reflecting surface The magnetic field generated at that location; At a point on the main reflective surface, As a secondary reflector, Let be the distance from a point on the sub-reflector surface to the feed source. ; The wave number is represented as: ; , The distance from a point on the primary reflector to a point on the secondary reflector. for The unit direction vector; Amplitude function on the sub-reflector surface; The rectangular coordinates of a point on the main reflecting surface. The rectangular coordinates of the feed source are... The length of the major axis of the ellipsoid, The length of the minor axis of the ellipsoid; The second integral expression for solving the far field from the current of the primary reflecting surface is: ； In the formula, Defined as the core integral term in the far-field expression; The spherical coordinate angle of the far-field observation direction. For the observation angle, It is the azimuth angle. The amplitude function on the main reflecting surface; The rectangular coordinates of a point on the principal reflecting surface; ; ; Main reflective surface, The focal length of the primary reflecting surface.

4. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 3, characterized in that, The amplitude function and phase function in the physical optics integral are linearly fitted, specifically as follows: The antenna's primary and secondary reflectors are discretized into multiple triangular mesh structures using triangular shell elements. Within each triangular mesh, the amplitude and phase functions during the two physical optical integration processes are linearly fitted. Amplitude function on the primary reflector The linear fitting expression is: ； Amplitude function on sub-reflector The linear fitting expression is: In the formula, The coefficients of the linear fit on the main reflective surface; , , The coefficients of the linear fit on the sub-reflector surface; Phase function on the primary reflector The linear fitting expression is: ； In the formula, The coefficients of the linear fit on the main reflective surface; For the observation angle, It is the azimuth angle; Focal length of the main reflecting surface; ; The wave number is represented as: ; The first fitting error is obtained based on the linear fitting expression of the phase function on the main reflection surface. e m Defined as: In the formula, The coefficients of the linear fit on the main reflective surface; Phase function on sub-reflector The linear fitting expression is: The second fitting error is obtained based on the linear fitting expression of the phase function on the sub-reflector surface. e s Defined as: ； In the formula, , , The coefficients are the linear fit coefficients on the sub-reflector surface.

5. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 4, characterized in that, Based on the equivalent wavenumber and equivalent wavelength, the phase fitting error introduced by the linear fitting in the two physical optical integrals is analyzed, specifically as follows: In the far-field main lobe and adjacent side lobe regions, the equivalent wavenumber of the second integral expression for solving the far-field from the main reflecting surface current is defined as: The corresponding equivalent wavelength is: , In the formula, The observation angle coefficient related to the number of sidelobes. The diameter of the primary reflecting surface in a double-reflecting surface. It almost remains constant; Calculate the first fitting error resulting from linear fitting of the phase function of the second integral expression. And define the first phase error coefficient as The first fitting phase error is ; The second fitting error is caused by linearly fitting the phase function of the first integral expression for solving the magnetic field of the main reflecting surface from the sub-reflecting surface current. And define the second phase error coefficient as The second fitting phase error is ; Based on the second fitting phase error, the influence of the fitting phase error of the sub-reflector on the magnetic field of the main reflector is obtained as follows: ； Based on the first fitting phase error, the influence of the fitting phase error of the main reflecting surface on the core integral term is expressed as follows: ； Based on the relationship between the phase fitting error and different operating wavelengths, when the operating wavelength is in the high-frequency band, the first phase error coefficient... Independent of frequency, and the second phase error coefficient It increases with increasing frequency.

6. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 5, characterized in that, A differentiated processing strategy is adopted, specifically: Keeping the mesh division of the primary reflector unchanged, and adaptively refining the mesh of the secondary reflector according to the second phase error coefficient, specifically: When the second phase error coefficient When the value exceeds a preset threshold, the triangular mesh is refined; wherein, the refinement includes reducing the side length of the triangular mesh to one-third of the original side length; wherein, the preset threshold is 0.

02.

7. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 5, characterized in that, Affine transformation and integration by parts are performed within the integration region of the structured mesh of the processed primary and secondary reflective surfaces, specifically as follows: The first integral expression for any structural mesh element is: ； Through affine transformation ; Transform any of its structural mesh elements into a standard integration interval: ； The expression for the second integral after the affine transformation is: ； In the formula, ； In the formula: The integral result over the standard structured mesh cell region derived by the integration by parts is a complex number; These are the linear fitting coefficients of the amplitude function within the grid cell of this structure. The linear fitting coefficients of the phase function within this grid cell are . The linear fitting coefficients of the phase function within the grid cell after combining like terms; The affine transformation coefficients that map arbitrary mesh elements to standard mesh elements. Focal length of the main reflecting surface These are real constants related to the linear fitting coefficients and affine transformations of the structural mesh elements; Equivalent wavenumber; Substitute the linearly fitted amplitude function and phase function into the second integral expression after affine transformation; By performing integral by parts over the standard integration interval on the second integral expression after substitution, a closed analytical expression for the far-field contribution of the mesh element of this structure is obtained. Based on the closed analytical expression of the far-field contribution of the structured grid cell, the far-field contributions of all structured grid cells are vector-superimposed to obtain the closed expression of the far-field radiation pattern of the ideal dual-reflector.

8. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 7, characterized in that, By solving the second integral expression within the standard integration interval using integration by parts, a closed analytical expression for the far-field contribution of the mesh element of this structure is obtained: 。 9. The rapid analysis method for electromechanical coupling of a dual-reflector antenna according to claim 7, characterized in that, Obtain the mesh node displacements caused by antenna structural deformation, and calculate the additional phase error introduced by the structural deformation at the mesh centroid, specifically: Obtain the z-direction deformation of each vertex of the triangular mesh obtained by finite element analysis in the structural mesh of the main reflector and the sub-reflector; The z-direction deformation at the centroid of each triangular mesh is calculated using vertex interpolation. ; Calculate the deformation in the z-direction Additional phase error introduced at the i-th grid centroid Its expression is: ,in The angle subtended at the centroid of the grid; The additional phase error As a phase factor Multiplying this into the closed-form expression of the far-field pattern of the ideal dual-reflector surface yields the far-field contribution of the deformed mesh. At this point, the deformed far-field contribution within the i-th mesh is... for: ; The far-field contribution of all the meshes after deformation is used to obtain the far-field radiation pattern of the deformed reflector antenna.

10. A rapid analysis system for electromechanical coupling of a dual-reflector antenna, characterized in that, include: The reconstruction module reconstructs the physical optical integral expression for far-field calculation based on the geometric relationship and coordinate transformation of the dual-reflector antenna. The linear fitting module discretizes the antenna reflector into multiple structural grid cells, and performs linear fitting on the amplitude function and phase function in the physical optical integral within each structural grid cell; The phase error coefficient acquisition module analyzes the phase fitting error introduced by the linear fitting in two physical optical integrations based on the equivalent wavenumber and equivalent wavelength; and obtains the phase error coefficient based on the relationship between the phase fitting error and different working wavelengths. The processing strategy design module adopts differentiated processing strategies for the structural mesh of the main reflector and the sub-reflector based on the phase error coefficient; The closed-form expression acquisition module obtains the closed-form expression of the far-field radiation pattern of the ideal dual-reflector by performing affine transformation and integration by parts in the integration region within the structured grid of the processed primary and secondary reflectors, solving the physical optics integral after linear fitting; The far-field radiation pattern acquisition module acquires the grid node displacement caused by antenna structure deformation, calculates the additional phase error introduced by the structural deformation at the grid centroid, and solves the deformed far-field radiation pattern containing the additional phase error based on the closed expression, thereby realizing rapid electromechanical coupling analysis of dual-reflector antennas.

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