A coupled ray and current-based antenna layout modeling analysis method

Abstract

This invention relates to the field of computational electromagnetics, specifically to an antenna layout modeling and analysis method based on coupled rays and current basis. The method includes: defining electrically small and electrically large regions of the electrically large carrier antenna layout target and generating mesh data; assembling the system matrix within the electrically small regions; accurately aggregating all illuminated areas within the electrically large regions using backward ray tracing technology; establishing a cyclic iterative mode for the electrically small and electrically large outer surface currents; obtaining the overall stable current distribution on the outer surface based on the residual convergence results of the currents in the electrically small regions; and finally solving for the antenna layout performance characteristics affected by the coupled electrically large carrier currents. This invention effectively improves the accuracy and efficiency problems of the traditional integral-ray hybrid method, and enhances the design efficiency of electrically large carrier antenna layouts.

Description

Technical Field

[0001] This invention relates to the field of computational electromagnetics, and to a calculation process and implementation method for the layout characteristics of electrically large carrier antennas, specifically an antenna layout modeling and analysis method based on coupled rays and current bases. Background Technology

[0002] With the increasing integration of modern wireless communication, radar detection, and electronic countermeasures systems, antennas often need to be mounted on large platforms such as aircraft, ships, and vehicles. The electromagnetic interaction between the antenna and the adjacent structure significantly alters the antenna's radiation characteristics, input impedance, and port-to-port transmission coefficients (S-parameters), directly affecting the overall electromagnetic compatibility performance of the system. Therefore, accurate and efficient electromagnetic simulation during the antenna layout design phase has become an indispensable part of system design.

[0003] Currently, electromagnetic simulation methods for antenna layout problems are mainly divided into three categories: full-wave numerical methods, including the finite element method (FEM), finite-difference time-domain method (FDTD), and method of moments (MoM), etc. These methods are based on rigorous solutions to Maxwell's equations and have the highest accuracy. However, for electrically large carriers (such as those with thousands of wavelengths), the number of unknowns required by full-wave methods is enormous, and memory consumption and computation time increase exponentially, which is often impractical in engineering. High-frequency approximation methods, including physical optics (PO), geometric diffraction theory (GTD), and bouncing ray method (SBR), etc., assume that the electromagnetic wave locally behaves as a plane wave, neglecting the fine phase terms of diffraction and multiple diffractions, resulting in fast computation speed and small memory footprint. However, they are essentially approximations and cannot accurately handle the complex structure of the antenna's near-field region, the feed port, and the fine radiation field distribution. To balance accuracy and efficiency, hybrid methods have emerged, including FEM-PO, FEM-SBR, and MoM-PO. Their basic idea is to divide the problem region into an "electrically small, fine-structure region" and an "electrically large, optical region," solving them using full-wave and high-frequency methods respectively, and coupling them through boundary conditions. The most representative technique is FEM-SBR (Finite Element-Boundary Integral-Bouncing Ray Method). This technique treats the antenna and its adjacent structures using the finite element-boundary integral method, and the carrier using the bouncing ray method, coupling them in the far-field region through Huygens surfaces. Despite its success, this method still has some limitations. For example, existing techniques typically default to unidirectional data transfer; that is, the current distribution of the electrically small structure is first solved using the finite element-boundary integral method, and then this current distribution is used as the incident source to illuminate the carrier, and the current distribution of the carrier is calculated using the bouncing ray method. This process does not consider the feedback effect of the induced current on the carrier on the near-field of the antenna. When the antenna is very close to the carrier (e.g., conformal antennas or low-profile antennas), this feedback effect is not negligible, leading to a significant decrease in computational accuracy. A common solution is to use the carrier mesh as the incident source and trace the effect on electrically small structures in the reverse direction. However, these electrically large carrier structures typically have a large mesh size, posing a significant risk to ray tracing efficiency. Furthermore, multiple bounces can cause the ray tube to diverge, especially for structures with curvature distortion. This problem has a severe impact on accuracy, making it impossible to accurately assess the influence of electrically large carriers on the antenna's radiation characteristics. Summary of the Invention

[0004] In view of the shortcomings of the prior art, the present invention aims to provide an antenna layout modeling and analysis method based on coupled rays and current basis, which effectively improves the accuracy and efficiency problems of the traditional integral ray hybrid method and improves the efficiency of electrically large carrier antenna layout design.

[0005] To achieve the purpose of this invention, the technical solution adopted is: an antenna layout modeling and analysis method based on coupled rays and current basis, including: S1, defining the electrically small and electrically large regions of the electrically large carrier antenna layout target and generating grid data.

[0006] S2. Assembly of the internal system matrix of the small electric region: The internal system matrix is ​​discretized using Whitney basis functions and filled according to the boundary conditions; the external surface is discretized using RWG basis functions according to the characteristics of Whitney basis functions, and the electric field integral equation is established according to the equivalence principle.

[0007] S3, Open University Area: Using backward ray tracing technology, accurately collect all irradiated areas.

[0008] S4. Establish a cyclic iterative mode for the outer surface current with small electrical charge and large electrical charge. Based on the residual convergence results of the current in the small electrical charge region, obtain the overall stable current distribution on the outer surface.

[0009] S5. Solve for the antenna layout performance characteristics affected by the coupled electrically large carrier current.

[0010] As an optimized solution of the present invention, step S1 includes: S1.1, when arranging the antenna, the electrically large carrier is divided into electrically small and electrically large regions according to the geometric structure and material parameter characteristics of the electrically large carrier.

[0011] S1.2 Set boundary conditions on the geometric surfaces of the electrically small and electrically large targets respectively.

[0012] S1.3. The electrically small and electrically large regions are divided into tetrahedral and triangular regions respectively to generate the mesh data information required for the solution.

[0013] As an optimized solution of the present invention, step S2 includes: S2.1, discretizing the internal region of electrical smallness using the Whitney basis function: .

[0014] Where: λ i For nodes i The centroid coordinates, λ j For nodes j The coordinates of the centroid, ▽λ i For nodes i The gradient of the barycentric coordinates, ▽λ j For nodes j The gradient of the centroid coordinates, W ij For Whitney node i and nodes j The corresponding basis functions.

[0015] The internal system matrix is ​​filled in according to the boundary conditions of the internal medium. The finite element governing equations of the internal system are as follows: .

[0016] in, V Let F(E) represent the internal space of the electric region, and let μ be the variational functional corresponding to the internal electric field E. r It is the relative permeability of the medium. ε r ∠ is the relative permittivity of the medium, and ∠ is the vector differential operator. k 0 is the free space wavenumber, d v Represents a volume element, j The imaginary unit, ω Let ω be the angular frequency, and μ0 be the free permeability. H It is a boundary surface s External equivalent magnetic field, It is a boundary surface s Outward normal unit vector, d s Represents a micro-element of area.

[0017] S2.2 On the outer surface of the electrically small region, discretize it using RWG basis functions, and satisfy the following relationship.

[0018] .

[0019] in: f n RWG basis functions defined on the nth edge of the outer surface. l n It is the length of that edge. W n For the outer surface n Whitney basis functions defined on the edge of the strip.

[0020] As an optimized solution of the present invention, step S2 further includes: S2.3, filling the outer surface matrix of the electrically small region according to the electromagnetic field equation satisfied by the outer surface boundary, and establishing the electric field integral equation at the boundary as follows: .

[0021] Where: E inc Let E be the incident electric field on the outer surface, and E be the electric field of the outer surface. L Operator representing the electric field integral equation, K 0() represents the principal value integral after removing singularities. η 0 is the free-space wave impedance. J n and E n These are the equivalent current and electric field coefficients to be solved.

[0022] As an optimized solution of the present invention, based on the algebraic relationship between the Whitney basis functions and the RWG basis functions on the boundary, the equivalent current and magnetic current are discretized into: .

[0023] in: J ( r ) is the venue r The equivalent current at that point, M ( r ) is the venue r The equivalent magnetic current at that point f n (r) is the RWG basis function at field point r. N s This represents the number of all edges on the boundary. J n and E n The equivalent current and electric field coefficient are unknown.

[0024] As an optimized solution of the present invention, in step S3, the geometric center of the electrically small region obtained in step S2 is used as the starting point of ray tracing; the geometric parameters of the electrically large region are used to construct a ray tracing engine; and the backward tracing method is used to determine the set of all irradiated triangles, including: S3.1, firstly, the geometric center of the electrically small region is calculated based on the geometric grid information of the electrically small region, and this is used as the emission source point of the ray tracing engine.

[0025] S3.2. Based on octree spatial partitioning, a ray tracing engine is built to accelerate the process. The geometric grid coordinates of the entire open-cell region are read to construct a global bounding box, which serves as the bounding domain of the octree root node. Rays enter from the root node, and AABB intersection detection is used to quickly determine which child nodes the ray passes through. Empty nodes with no intersection are skipped, and only the child blocks along the ray path are entered. The ray sinks down layer by layer to the leaf node, and only the triangular facets stored in the current leaf are retrieved for intersection calculation. All intersecting facets are collected as the effective illumination area of ​​the current ray, which serves as the target for subsequent antenna radiation.

[0026] As an optimized solution of the present invention, step S4 includes: S4.1, using LU decomposition to decompose the sparse matrix inside the small electric region and substituting it into the electric field integral equation established at the boundary to solve.

[0027] S4.2 The initial current distribution in the electrically large region can be obtained directly by solving the current distribution in the electrically small region.

[0028] S4.3 Establish a cyclic iterative process for the current in the electrically small and electrically large regions. Based on the current distribution on the electrically large carrier, calculate the excitation effect of the carrier current on the superposition of the basis functions on the outer surface of the antenna. The specific formula is as follows: .

[0029] in:b k It is the right-hand term of the k-th iteration. b 0 It is the initial right-hand term. f m It is the RWG basis function of the outer surface of the electrically small region. E The electric field generated by the surface current in the electrically large region in the electrically small region is specifically represented as follows.

[0030] .

[0031] in: j The imaginary unit, k 0 It is the free space wavenumber. η 0 It is free-space wave impedance. J d Let r represent the current density vector at a point in a triangular mesh of an electric field carrier, where r is the field point coordinate and r' is the source point coordinate. ds´ is the infinitesimal area element of the source point, and ▽´ is the gradient operator of the source point coordinates r´.

[0032] As an optimized solution of the present invention, step S4 further includes: ending the iteration after the outer surface current of the electrically small region stabilizes, with the convergence formula as follows: .in: δ (k) For the first k The residual of the nth iteration, ||·|| represents the vector norm. I k Representing the k When the surface current density of the electrically small region is less than a preset threshold or greater than the maximum number of iterations, the iteration ends, and the surface current of the electrically small region is considered to be stable.

[0033] As an optimized solution of the present invention, step S5 includes: digitally modeling based on an electromagnetic simulation platform to construct the geometric structure of the electrically large carrier antenna layout; generating tetrahedral and triangular meshes based on the mesh generation tool of the electromagnetic simulation platform; setting boundary conditions and calling the electrically large carrier antenna layout characteristic analysis solver; substituting the iteratively converged surface current of the electrically small structure into the system matrix, representing the surface electric field with the surface current and substituting it into the electric field integral equation established at the boundary to solve; substituting the solved surface current into the relationship with the surface electric field to calculate the internal and boundary electric field distributions.

[0034] As an optimized solution of the present invention, in step S5, the stabilized outer surface current is substituted into the relationship between the electric field and the outer surface current to solve for the internal and boundary electric fields: .

[0035] in: E i It is the unknown coefficient of the electric field on the edge of the small body, { E s} is the vector of unknown electric field coefficients at the outer surface boundary of the antenna, and [B] is the matrix of coupling coefficients between the electrically small region and its boundary. J s} is the equivalent current excitation source vector on the electrically small boundary surface. b i Internal antenna feed excitation source vector.

[0036] This invention offers several advantages: it improves the efficiency and accuracy of the integral-ray-based hybrid algorithm for solving electrically large carrier antenna layouts. Traditional methods for simulating the performance of electrically large carrier antenna layouts typically require unidirectional coupling, neglecting the influence of carrier current on the antenna's radiation characteristics. Even with multiple ray bounces, the ray tracing process is extremely time-consuming, and ray tubes are prone to splitting, leading to reduced accuracy. This invention, based on a coupled ray-current basis, can rapidly iterate the interaction between the coupled antenna and the electrically large carrier based on the ray tube current set from a single bounce, obtaining a stable current distribution. This invention reduces the time-consuming ray tracing caused by multiple bounces, and importantly, avoids the accuracy impact caused by ray tube splitting, thus enhancing the solution capability of the hybrid algorithm. Attached Figure Description

[0037] The present invention will now be described in further detail with reference to the accompanying drawings and practical examples.

[0038] Figure 1 This is a schematic diagram of the process of the present invention.

[0039] Figure 2 This is a schematic diagram of the geometric structure of the present invention.

[0040] Figure 3 This is a schematic diagram of the X-ray tube tracking and X-ray tube splitting of the present invention.

[0041] Figure 4 This is a schematic diagram of the frequency sweep result of the single antenna S11 of the present invention.

[0042] Figure 5 This is a schematic diagram comparing the results of different algorithms S11 in this invention. Detailed Implementation

[0043] The terms "first," "second," "third," "fourth," etc. (if present) in the specification, claims, and accompanying drawings of this invention are used to distinguish similar objects and are not necessarily used to describe a specific order or sequence. It should be understood that such data can be interchanged where appropriate so that the embodiments described herein can be implemented in orders other than those illustrated or described herein. Furthermore, the terms "comprising" or "having" and any variations thereof are intended to cover a non-exclusive inclusion; for example, a process, method, system, product, or apparatus that comprises a series of steps or units is not necessarily limited to those steps or units explicitly listed, but may include other steps or units not explicitly listed or inherent to such processes, methods, products, or apparatus.

[0044] For ease of understanding, the specific process of the embodiments of the present invention is described below. Please refer to [link / reference]. Figure 1 This invention provides an antenna layout modeling and analysis method based on coupled rays and current bases, including: Step 1, defining the electrically small and electrically large regions of the electrically large carrier antenna layout target and generating grid data; specifically including: S1.1, during antenna layout, the electrically large carrier is divided into electrically small and electrically large regions according to the geometric structure and material parameter characteristics of the electrically large carrier.

[0045] S1.2 Set boundary conditions on the geometric surfaces of the electrically small and electrically large targets respectively.

[0046] S1.3. The electrically small and electrically large regions are divided into tetrahedral and triangular regions respectively to generate the mesh data information required for the solution.

[0047] The embodiments of this invention are based on the advanced full-wave electromagnetic simulation platform Rainbow Studio EM. Geometric modeling of the electrically large carrier and antenna target is performed, boundary conditions and material properties for different regions are set, and the correctness of the case parameter settings is checked. Tetrahedral and triangular meshes that meet the solver requirements are generated using Rainbow Studio EM. The electrically large carrier and antenna regions are classified as electrically small / electrically large, and automated mesh generation technology is employed. This allows for differentiated discretization strategies for regions with different electrical dimensions, significantly reducing the number of unknowns while ensuring computational accuracy, and effectively improving the computational efficiency of subsequent hybrid solutions.

[0048] Step 2: Call the coupled ray-current basis solver to assemble the system matrix of the small electric region.

[0049] In embodiments of the present invention, based on a coupled ray-current-based solver, the unknowns in the electrically small and electrically large regions are processed separately, such as... Figure 1 As shown. Within the electrically small region, discretization is performed using the Whitney basis function: Wherein: λ i For nodes iThe barycenter coordinates, and the basis functions belong to H( curl The space ensures the continuity of the tangential component at the element interface; λ j For nodes j The coordinates of the centroid, ▽λ i For nodes i The gradient of the barycentric coordinates, ▽λ j For nodes j The gradient of the centroid coordinates, W ij For Whitney node i and nodes j The corresponding basis functions.

[0050] The internal system matrix is ​​filled in according to the boundary conditions of different internal media. The finite element governing equations of the internal system are as follows: .

[0051] in, V Let F(E) represent the internal space of the electric region, and let μ be the variational functional corresponding to the internal electric field E. r It is the relative permeability of the medium. ε r ∠ is the relative permittivity of the medium, and ∠ is the vector differential operator. k 0 is the free space wavenumber, d v Represents a volume element, j The imaginary unit, ω Let ω be the angular frequency, and μ0 be the free permeability. H It is a boundary surface s External equivalent magnetic field, It is a boundary surface s Outward normal unit vector, d s Represents a micro-element of area.

[0052] On the outer surface of the electrically small region, discretization is performed using RWG basis functions, and the following relationship is satisfied: .

[0053] in: f n RWG basis functions defined on the nth edge of the outer surface. l n It is the length of that edge. W n For the outer surface n The Whitney basis functions defined on the edges of the outer surface must be matched with the RWG basis functions to ensure the continuity of the field. Based on the electromagnetic field equations satisfied by the outer surface boundary, the outer surface matrix filling the electrically small region is used to establish the electric field integral equation at the boundary as follows: .

[0054] Where: E inc Let E be the incident electric field on the outer surface, and E be the electric field of the outer surface. L Operator representing the electric field integral equation, K 0() represents the principal value integral after removing singularities. η 0 is the free-space wave impedance. J M and M are the equivalent current and magnetic current on the outer surface of the electric region.

[0055] Based on the algebraic relationship between the Whitney basis functions and the RWG basis functions on the boundary, the equivalent current and magnetic current are discretized as follows: .

[0056] in: J ( r ) is the venue r The equivalent current at that point, M ( r ) is the venue r The equivalent magnetic current at that point f n (r) is the RWG basis function at field point r. N s This represents the number of all edges on the boundary. J n and E n These are the equivalent current and electric field coefficients to be solved. By matching and discretizing the Whitney basis functions and the RWG basis functions, seamless coupling between the finite element region and the boundary integral equation region is achieved, ensuring the tangential continuity of the electromagnetic field at the interface and avoiding numerical errors caused by basis function mismatch in traditional methods. At the same time, treating the equivalent current and magnetic current as unknowns effectively reduces the dimensionality of the problem and improves the assembly efficiency of the system matrix.

[0057] Step 3, Open University Area: Using backward ray tracing technology, accurately gather all irradiated areas.

[0058] S3.1 First, calculate the geometric center of the electric small region based on the geometric mesh information of the electric small region, and use it as the emission source point of the ray tracing engine.

[0059] S3.2. A ray-tracking engine is built using octree spatial partitioning to accelerate ray tracing. The geometric mesh coordinates of the entire open-cell region are read, and a global bounding box is constructed as the bounding domain of the octree root node. Rays enter from the root node, and AABB intersection detection is used to quickly determine which child nodes the ray passes through, skipping empty nodes with no intersection and only entering the child blocks along the ray's path. Rays descend layer by layer to the leaf nodes, retrieving only the triangular faces stored within the current leaf node for intersection calculations. For the few selected triangular meshes, intersection calculations are performed, and all valid illumination areas are aggregated. Here, the Fock current is the induced current at the center of the triangle in the ray tube illumination area.

[0060] In embodiments of the present invention, such as Figure 3 As shown, based on step 2, the geometric center of the electrically small region can be obtained. Using this coordinate as the incident source point, an advanced ray tracing engine can quickly aggregate all carrier region meshes within the antenna radiation range. Unlike traditional forward tracing, backward tracing is used here, starting from the geometric center of the electrically small region to determine visibility in reverse, avoiding the calculation of a large number of invalid rays in traditional forward tracing and reducing ray tracing time by more than an order of magnitude. At the same time, by quickly aggregating the irradiated area, the local areas on the electrically large carrier affected by antenna radiation can be accurately located, providing a precise excitation source distribution for subsequent current iterations, significantly improving the overall simulation efficiency.

[0061] Step 4: Establish a cyclic iterative mode for the external surface current with small electrical properties and large electrical properties. Based on the residual convergence results of the current in the small electrical region, obtain the overall stable current distribution on the external surface.

[0062] Step S4 includes: S4.1, using LU decomposition to solve the sparse matrix inside the small electric region and substituting it into the electric field integral equation established at the boundary.

[0063] First, the antenna boundary current distribution is calculated without considering the influence of electrically large carriers. Equations regarding the interior and boundary of the electrically small region were established in step 2. Combining these two equations, the finite element-boundary element system equations are obtained as follows: .

[0064] Where: A matrix block is the constitutive relation matrix of the finite element method. A ii Here is the stiffness matrix within the electrically small region. A is and A si The coupling matrix is ​​the internal and boundary matrix of the electrically small region. A ss Here is the stiffness matrix on the boundary of the electrically small region. b i Internal antenna feed excitation source vector, E i It is the unknown coefficient of the electric field on the edge of the small body. E s It is the unknown coefficient of the electric field on the electric small boundary surface. J s It is the equivalent current excitation source vector on the electrically small boundary surface. B The matrix blocks are the coupling terms of the boundary electric field and current, and both of these matrix blocks are sparse matrices.

[0065] C ss The matrix represents the radiation impedance matrix of the current on the boundary.D ss The matrix is ​​the scattering feedback matrix of the electric field by the equivalent magnetic current on the boundary. The definitions of the C matrix and the D matrix are as follows.

[0066] .

[0067] .

[0068] in, sm Let m represent the m-th triangle on the boundary, and sn represent the n-th triangle on the boundary. C mm These are the radiation impedance matrix elements corresponding to the equivalent currents on the boundary. D mm These are the elements of the scattering feedback matrix of the electric field by the equivalent magnetic current at the boundary. j The imaginary unit, k 0 It is the free space wavenumber. η 0 It is free-space wave impedance. f n (r´) is the RWG basis function at the source point r´. f m (r) represents the RWG basis function at field point r, where r is the field point coordinate and r' is the source point coordinate. G 0 is a free-space scalar Green's function. ds´ It is a source point area infinitesimal element. ds It is a field point area infinitesimal element, and ▽´ is the gradient operator with respect to the source point coordinates r´. w n It is the coupling coefficient of the tangential electric field generated by the equivalent magnetic current at the boundary.

[0069] Performing LU decomposition on the constitutive sparse matrix of the finite element in the equation, the electric field... Available { J s The following formula can be used to calculate: A ]= [ L ][ U ]; .

[0070] in,[ A ] is the total matrix of the electrically small region finite element sparse system, [ L ]yes[ A The lower triangular identity matrix after LU decomposition of the matrix is ​​[ U ]yes[ A The matrix after LU decomposition is an upper triangular matrix. E i It is the unknown coefficient of the electric field on the edge of the small body, { E s} is the vector of unknown electric field coefficients at the outer surface boundary of the electrically small region. B ] is the coupling coefficient matrix of the electrically small region volume and its boundary { J s} is the equivalent current excitation source vector on the electrically small boundary surface. b i The internal antenna feed excitation source vector is used to substitute the above equation into the electric field integral equation established at the boundary, and the solution is obtained to obtain the current distribution on the outer surface of the antenna without considering the influence of the carrier.

[0071] By performing LU decomposition on the finite element constitutive matrix and eliminating the internal degrees of freedom in advance, the scale of unknowns in the boundary integral equation is significantly reduced. This makes the solution of the current distribution of electrically large antennas acceptable in terms of computational resources and time consumption. Furthermore, the antenna's own current distribution can be solved independently without considering the influence of the electrically large carrier, realizing the decoupled analysis of the antenna-carrier coupling problem. This facilitates the separate evaluation of the antenna's intrinsic radiation characteristics and also provides reliable initial values ​​for the iterative algorithm, accelerating the convergence speed of subsequent coupling iterations.

[0072] S4.2 The initial current distribution in the electrically large region can be obtained directly by solving the current distribution in the electrically small region.

[0073] Let the equivalent current excitation source vector on the electrically small boundary surface be { J s The current distribution in the open university region is determined by the initial current distribution { J s At the center point of the Open University's regional grid The magnetic field generated at that location is obtained, and the specific formula is as follows: .

[0074] in: J d This represents the Fock current vector at a point in a triangular grid that is illuminated on an electrical carrier. n The outward normal unit vector of the electrical engineering carrier mesh. L H It is a magnetic field integral operator. J s ∠ is the equivalent current excitation source vector on the electrically small boundary surface, and ▽ is the vector differential operator. Represents the free-space scalar Green's function, which describes the field propagation from the source to the field. ds´ It is a source surface micro-element.

[0075] By utilizing the equivalence principle and the magnetic field integral equation, the antenna current in the electrically small region is used as the excitation source to quickly calculate the initial current distribution induced by it on the surface of the electrically large carrier. This realizes the physical process mapping from "antenna source" to "carrier response", ensuring that the initial current estimation conforms to the electromagnetic scattering mechanism and providing a physically reasonable starting point for iterative loops.

[0076] S4.3 Establish a cyclic iterative process for the current in the electrically small and electrically large regions. Based on the current distribution on the electrically large carrier, calculate the excitation effect of the carrier current on the superposition of the basis functions on the outer surface of the antenna. The specific formula is as follows: .

[0077] in: b k It is the right-hand term of the k-th iteration. b 0 It is the initial right-hand term. f m It is the RWG basis function of the outer surface of the electrically small region. E The electric field generated by the surface current in the electrically large region in the electrically small region is specifically represented as follows.

[0078] .

[0079] in: j The imaginary unit, k 0 It is the free space wavenumber. η 0 It is free-space wave impedance. J d Let r represent the current density vector at a point in a triangular mesh of an electric field carrier, where r is the field point coordinate and r' is the source point coordinate. ds´ is the infinitesimal area element of the source point, and ▽´ is the gradient operator of the source point coordinates r´.

[0080] The iteration ends when the surface current of the electrically small region stabilizes. The convergence formula is as follows: .

[0081] in: δ (k) For the first k The residual of the nth iteration, ||·|| represents the vector norm. I k Representing the k The surface current density of the small electric region in the next iteration, when δ (k) Less than the preset threshold or kWhen the number of iterations exceeds the maximum, the iteration ends, and the surface current of the electrically small region is considered to have stabilized. By establishing a bidirectional coupling iteration mechanism between electrically small and electrically large regions, the multiple reflection effects between the antenna and the carrier are accurately captured, compensating for the deficiency of neglecting carrier secondary scattering in single approximation calculations. Using the relative residual norm as the convergence criterion and setting dual convergence criteria (residual threshold and maximum number of iterations) ensures numerical stability while automatically adapting to scenarios with different coupling strengths. This guarantees the accuracy and controllability of the calculation results and avoids the risk of iteration non-convergence in strongly coupled scenarios, enhancing the robustness and reliability of the algorithm in complex engineering applications. It ensures that the final current distribution satisfies the electromagnetic self-consistency condition, thereby accurately predicting the actual impact of carrier loading on antenna radiation performance.

[0082] Step 5: Based on the stable current distribution on the outer surface of the electrically small region, solve for the antenna layout performance characteristics affected by the coupled electrically large carrier current; using the finally converged stable current distribution, calculate the antenna's radiation pattern, gain, input impedance and other key performance indicators. This can accurately quantify the actual engineering impact of the electrically large carrier on the antenna layout, such as pattern distortion, gain reduction and impedance mismatch, providing high-precision simulation basis and decision support for the optimized layout of the antenna on complex platforms.

[0083] An embodiment of the present invention takes the antenna layout model of a certain fighter jet as an example. This model is built based on the domestically developed advanced electromagnetic simulation platform Rainbow Studio, such as... Figure 2 As shown, tetrahedral and triangular partitioning is used. Initially, the surface current of the aircraft is ignored, and the initial effect on the antenna is calculated. The current distribution in the electrically small region without considering the aircraft surface current is obtained. Then, the surface current in the electrically small region is used as a secondary radiation source to calculate the surface current distribution in the electrically large region. The surface current in the electrically large region is then used as a secondary radiation source to calculate the current in the electrically small region considering the aircraft surface current. This process is repeated until the residual of the surface current in the electrically small region between two consecutive calculations satisfies the convergence condition. Figure 3 As shown, this method avoids the problem of ray tube splitting caused by repeated bouncing in traditional schemes; the final antenna S11 parameter characteristics affected by the coupled fighter jet current represent the port matching between the antenna and the overall fighter jet system, and can guide designers to adjust the antenna layout. Figure 4 The figure shows the S11 frequency sweep results under single-antenna radiation. It can be seen from the figure that the antenna achieves optimal impedance matching around 0.9 GHz, but suffers from severe impedance mismatch in the low-frequency range and gradually deteriorates in the high-frequency range, causing the antenna to deviate from its resonant state. A comparison is made between the traditional ray scheme and the full-wave solution scheme. Figure 5The results clearly show that after loading an electrically large carrier, S11 deteriorates from -26 dB to approximately -5 dB, and the resonant point completely disappears. This indicates that the carrier severely disturbs the antenna impedance matching. The curves from the full-wave method and the ray-current iteration method are highly consistent (at 0.9 GHz: -5.31 dB vs -5.45 dB), verifying that the accuracy of the iteration method is consistent with that of the full-wave method. The pure ray method deviates significantly from the full-wave method, proving that the electrically large carrier has a significant impact on the antenna, and the current coupling effect between the two must be considered in antenna layout analysis. The S-parameter results of this invention are closer to the accuracy of the full-wave scheme, effectively improving the accuracy of solving electrically large carrier antenna layouts using hybrid finite element-ray tracing.

[0084] The above-described embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for antenna layout modeling and analysis based on coupled rays and current basis, characterized in that, include: S1. Determine the electrically small and electrically large regions of the electrically large carrier antenna layout target and generate grid data; S2. Assembly of the internal system matrix of the small electric region: The internal system matrix is ​​discretized using Whitney basis functions and filled according to the boundary conditions; the external surface is discretized using RWG basis functions according to the characteristics of Whitney basis functions, and the electric field integral equation is established according to the equivalence principle. S3, Open University Area: Using backward ray tracing technology, accurately gather all irradiated areas; S4. Establish a cyclic iterative mode for the outer surface current with small electrical strength and large electrical strength. Based on the residual convergence results of the current in the small electrical strength region, obtain the overall stable current distribution on the outer surface. S5. Solve for the antenna layout performance characteristics affected by the coupled electrically large carrier current.

2. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 1, characterized in that: Step S1 includes: S1.1 When laying out the antenna, the electrically large carrier is divided into electrically small and electrically large regions according to the geometric structure and material parameters of the electrically large carrier. S1.2 Set boundary conditions on the geometric surfaces of the electrically small and electrically large targets respectively; S1.

3. The electrically small and electrically large regions are divided into tetrahedral and triangular regions respectively to generate the mesh data information required for the solution.

3. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 2, characterized in that, Step S2 includes: S2.

1. Discretize the region of small electrical energy using Whitney basis functions: Wherein: λ i For nodes i The centroid coordinates, λ j For nodes j The coordinates of the centroid, ▽λ i For nodes i The gradient of the barycentric coordinates, ▽λ j For nodes j The gradient of the centroid coordinates, W ij For Whitney node i and nodes j The corresponding basis functions; fill the internal system matrix according to the boundary conditions of the internal medium, and the finite element governing equations of the internal system are as follows: ； in, V Let F(E) represent the internal space of the electric region, and let μ be the variational functional corresponding to the internal electric field E. r It is the relative permeability of the medium. ε r ∠ is the relative permittivity of the medium, and ∠ is the vector differential operator. k 0 is the free space wavenumber, d v Represents a volume element, j The imaginary unit, ω Let ω be the angular frequency, and μ0 be the free permeability. H It is a boundary surface s External equivalent magnetic field, It is a boundary surface s Outward normal unit vector, d s Represents a micro-element of area; S2.2 On the outer surface of the electrically small region, discretize using RWG basis functions, and satisfy the following relationship: ; in: f n RWG basis functions defined on the nth edge of the outer surface. l n It is the length of that edge. W n For the outer surface n Whitney basis functions defined on the edge of the strip.

4. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 3, characterized in that, Step S2 also includes: S2.3, filling the outer surface matrix of the electrically small region according to the electromagnetic field equation satisfied by the outer surface boundary, and establishing the electric field integral equation at the boundary as follows: ; where: E inc Let E be the incident electric field on the outer surface, and E be the electric field of the outer surface. L Operator representing the electric field integral equation, K 0() represents the principal value integral after removing singularities. η 0 is the free-space wave impedance. J M and M are the equivalent current and magnetic current on the outer surface of the electric region.

5. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 4, characterized in that, Based on the algebraic relationship between the Whitney basis functions and the RWG basis functions on the boundary, the equivalent current and magnetic current are discretized as follows: ;in: J ( r ) is the venue r The equivalent current at that point, M ( r ) is the venue r The equivalent magnetic current at that point f n (r) is the RWG basis function at field point r. N s This represents the number of all edges on the boundary. J n and E n These are the equivalent current and electric field coefficients to be solved.

6. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 5, characterized in that: In step S3, the geometric center of the electrically small region obtained in step S2 is used as the starting point for ray tracing; A ray-tracking engine was constructed using the geometric parameters of the Open University region. Using a backward tracing method, the set of all illuminated triangles is determined, including: S3.1 First, calculate the geometric center of the electric small region based on the geometric mesh information of the electric small region, and use it as the emission source point of the ray tracing engine; S3.

2. Based on octree spatial partitioning, a ray tracing engine is built to accelerate the process. The geometric grid coordinates of the entire open-cell region are read to construct a global bounding box, which serves as the bounding domain of the octree root node. Rays enter from the root node, and AABB intersection detection is used to quickly determine which child nodes the ray passes through. Empty nodes with no intersection are skipped, and only the child blocks along the ray path are entered. The ray sinks down layer by layer to the leaf node, and only the triangular facets stored in the current leaf are retrieved for intersection calculation. All intersecting facets are collected as the effective illumination area of ​​the current ray, which serves as the target for subsequent antenna radiation.

7. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 6, characterized in that: Step S4 includes: S4.

1. Use LU decomposition to solve the sparse matrix inside the small electric region and substitute it into the electric field integral equation established at the boundary. S4.2 The initial current distribution in the electrically large region can be obtained directly by solving the current distribution in the electrically small region; S4.3 Establish a cyclic iterative process for the current in the electrically small and electrically large regions. Based on the current distribution on the electrically large carrier, calculate the excitation effect of the carrier current on the superposition of the basis functions on the outer surface of the antenna. The specific formula is as follows: ;in: b k It is the right-hand term of the k-th iteration. b 0 It is the initial right-hand term. f m It is the RWG basis function of the outer surface of the electrically small region. E The electric field generated by the surface current in the electrically large region at the electrically small region is specifically represented as follows: ； in: j The imaginary unit, k 0 It is the free space wavenumber. η 0 It is free-space wave impedance. J d Let r represent the current density vector at the midpoint of the triangular mesh of the electric field carrier, where r is the coordinate of the field point and r' is the coordinate of the source point. ds´ The source point area is a infinitesimal element, and ▽´ is the gradient operator with respect to the source point coordinates r´. This represents the Green's function for free space scalars.

8. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 7, characterized in that, Step S4 also includes: The iteration ends when the surface current of the electrically small region stabilizes. The convergence formula is as follows: ;in: δ (k) For the first k The residual of the nth iteration, ||·|| represents the vector norm. I k Representing the k When the surface current density of the electrically small region is less than a preset threshold or greater than the maximum number of iterations, the iteration ends, and the surface current of the electrically small region is considered to be stable.

9. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 8, characterized in that: Step S5 includes: Digital modeling based on an electromagnetic simulation platform was used to construct the geometric structure of the electrically large carrier antenna layout. Tetrahedral and triangular meshes were generated using the mesh generation tool on the electromagnetic simulation platform. Boundary conditions were set, and the solver for the characteristic analysis of the electrically large carrier antenna layout was called. The iteratively converged surface current of the electrically small structure was substituted into the system matrix, and the surface electric field was expressed by the surface current and substituted into the electric field integral equation established at the boundary to solve. The surface current obtained by the solution was substituted into the relationship with the surface electric field to calculate the internal and boundary electric field distribution.

10. The antenna layout modeling and analysis method based on coupled rays and current basis according to claim 9, characterized in that: In step S5, the stabilized outer surface current is substituted into the relationship between the electric field and the outer surface current to solve for the internal and boundary electric fields: ;in: E i It is the unknown coefficient of the electric field on the edge of the small body, { E s } is the vector of unknown electric field coefficients at the outer surface boundary of the antenna, and [B] is the matrix of coupling coefficients between the electrically small region and its boundary. J s } is the equivalent current excitation source vector on the electrically small boundary surface. b i Internal antenna feed excitation source vector.

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