Topology reconstruction method and system of filter coupling matrix, terminal and medium

Abstract

The invention discloses a topology reconstruction method and system for a filter coupling matrix, a terminal and a medium, and the method comprises the steps: obtaining a random coupling matrix and a random capacitance matrix of a target topology, and obtaining a transformation matrix according to the random coupling matrix and the random capacitance matrix; if the target topology contains frequency-dependent coupling, singular value decomposition and rotation matrix decomposition are carried out on the transformation matrix to obtain a product of a scaling matrix and a product of a rotation matrix, and a reconstruction path is obtained according to the product of the scaling matrix and the product of the rotation matrix; establishing an objective function, and performing gradient derivation according to the objective function and the reconstruction path to obtain an analytic gradient; and adjusting transformation parameters according to the analytic gradient and the target function to obtain a target topological coupling matrix. According to the invention, the calculation efficiency of the frequency-dependent coupling-containing target coupling matrix in the target topology can be improved.

Description

Technical Field

[0001] The present application relates to the field of microwave communications and filter technology, and in particular to a topology reconstruction method, system, terminal, and computer-readable storage medium for a filter coupling matrix. Background Art

[0002] With the development and popularization of fifth-generation mobile communication technology, the requirements for filters are becoming increasingly stringent, such as flexible topology, steep roll-off, significant out-of-band suppression, and compact device size. In order to meet different physical layouts and responses, different topologies need to be adopted. As an abstract representation of the filter topology, the coupling matrix plays an important role in filter synthesis, design, and tuning. In general, the lateral coupling matrix can be easily obtained given the filter order, transmission zero point, and return loss value. Then, through a series of fixed-order rotation transformations (also called reconstruction paths), the coupling matrix can be reconfigured into other classic topologies such as folded type, wheel type, triangular element, and quadrangular element. Although the coupling matrix rotation transformation has high transformation efficiency, only a few reconstruction paths for traditional topologies are known.

[0003] Research on filter coupling matrix reconstruction paths has long been a hot topic in this field. While existing methods can reconstruct a wider range of topologies, they require only cross-coupling in the target topology and require pre-solution using existing numerical methods. Topology reconstruction for frequency-dependent coupling and non-resonant nodes remains unresolved.

[0004] Therefore, the existing technology still needs to be improved and developed. Summary of the Invention

[0005] The main purpose of this application is to provide a topology reconstruction method, system, terminal and medium for a filter coupling matrix, aiming to solve the problem in the prior art that the reconstruction path of the filter coupling matrix requires only cross-coupling in the target topology and needs to be pre-solved with the help of numerical methods, but cannot handle topology reconstruction containing frequency-varying coupling, resulting in low computational efficiency.

[0006] A first aspect of an embodiment of the present application provides a topological reconstruction method for a filter coupling matrix, and the topological reconstruction method for the filter coupling matrix includes the following steps: obtaining a random coupling matrix and a random capacitance matrix of a target topology, and obtaining a transformation matrix based on the random coupling matrix and the random capacitance matrix; if the target topology contains frequency-varying coupling, performing singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain the product of a scaling matrix and a product of a rotation matrix, and obtaining a reconstruction path based on the product of the scaling matrix and the product of the rotation matrix; establishing an objective function, and performing gradient derivation based on the objective function and the reconstruction path to obtain an analytical gradient; adjusting the transformation parameters based on the analytical gradient and the objective function to obtain a target topological coupling matrix.

[0007] Optionally, in one embodiment of the present application, the transformation matrix is ​​obtained according to the random coupling matrix and the random capacitance matrix, specifically including: obtaining a completely diagonalized coupling diagonal matrix and a capacitance diagonal matrix according to the random coupling matrix and the random capacitance matrix; obtaining a transverse topological coupling matrix and a transverse topological capacitance matrix according to the coupling diagonal matrix and the capacitance diagonal matrix; obtaining a transformation matrix according to the transverse topological coupling matrix and the transverse topological capacitance matrix.

[0008] Optionally, in one embodiment of the present application, the transformation matrix is ​​obtained according to the random coupling matrix and the random capacitance matrix, and then the method further includes: if the target topology does not contain frequency-variable coupling, performing rotation matrix decomposition on the transformation matrix to obtain the product of the rotation matrix, and obtaining a reconstruction path according to the product of the rotation matrix; the reconstruction path is expressed as:

[0009]

[0010] Among them, n is the number of rotation transformations, R m (θ m ) is the mth rotation angle θ m The rotation transformation, M f is the classical topological coupling matrix, M T is the target topology coupling matrix.

[0011] Optionally, in one embodiment of the present application, performing singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain the product of the scaling matrix and the product of the rotation matrix specifically includes: performing singular value decomposition on the transformation matrix to obtain a singular value diagonal matrix and a rotation matrix; decomposing the singular value diagonal matrix into the product of the scaling matrices, and the product of the scaling matrices is expressed as:

[0012] Among them, S i is the scaling matrix, αi is the scaling factor;

[0013] The rotation matrix is ​​decomposed into the product of rotation matrices, which is expressed as:

[0014] Among them, R ij is the rotation matrix, (i, j) is the rotation center, θ ij is the rotation angle.

[0015] Optionally, in one embodiment of the present application, the reconstruction path is expressed as:

[0016]

[0017] Among them, M T is the target topological coupling matrix, R i (θ i ) is the rotation angle θ i The rotation matrix acting on one side, R j (θ j ) is the rotation angle θ j The rotation matrix acting on the other side, S l (α l ) is the scaling factor α l The scaling matrix, x and z are the number of rotation transformations, y is the number of scaling transformations, M f is the classical topological coupling matrix, C T is the target topology capacitance matrix, C f is the classical topological capacitance matrix, and T represents the transpose.

[0018] Optionally, in one embodiment of the present application, the objective function is established, and the gradient is derived based on the objective function and the reconstruction path to obtain an analytical gradient, specifically including: simultaneously constraining the non-diagonal elements of the target topological coupling matrix and the target topological capacitance matrix to be zero to obtain the objective function; and deriving the analytical gradient of the objective function with respect to the rotation angle and scaling factor based on the reconstruction path.

[0019] Optionally, in one embodiment of the present application, the objective function is expressed as:

[0020] M T (i,j)=0,when(i,j)∈T M ;

[0021] C T (i,j)=0,when(i,j)∈T C ;

[0022] Among them, M Tis the target topological coupling matrix, (i, j) is the rotation center index acting on the (i, j)th row and jth column, T M is the node index of the element that should be 0 in the target topology coupling matrix, C T is the target topology capacitance matrix, T C is the node index of the element that should be 0 in the target capacitance matrix;

[0023] The analytical gradient is expressed as:

[0024]

[0025] in, is the objective function M T About the rotation angle θ i The partial derivative of R k is the rotation matrix acting on the kth rotation operation, is the rotation matrix R i About the rotation angle θ i The derivative of R j is the rotation matrix acting on the jth rotation operation, M f is the classical topological coupling matrix, S l is the scaling matrix acting on the lth one, x and z are the number of rotation transformations, y is the number of scaling transformations, C f is a classical topological capacitor matrix; is the objective function M T About the scaling factor α l The partial derivative of α l is the lth scaling factor, R i is the rotation matrix acting on the i-th rotation operation, is the scaling matrix S l About the scaling factor α l The derivative of , T represents the transpose.

[0026] A second aspect of an embodiment of the present application further provides a topology reconstruction system for a filter coupling matrix, wherein the topology reconstruction system for the filter coupling matrix includes:

[0027] a transformation matrix calculation module, configured to obtain a random coupling matrix and a random capacitance matrix of a target topology, and obtain a transformation matrix according to the random coupling matrix and the random capacitance matrix;

[0028] a reconstruction path determination module, configured to, if the target topology contains frequency-variant coupling, perform singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain a product of a scaling matrix and a product of a rotation matrix, and obtain a reconstruction path based on the product of the scaling matrix and the product of the rotation matrix;

[0029] An analytical gradient derivation module is used to establish an objective function and perform gradient derivation based on the objective function and the reconstruction path to obtain an analytical gradient;

[0030] The target coupling matrix output module is used to adjust the transformation parameters according to the analytical gradient and the objective function to obtain the target topological coupling matrix.

[0031] The third aspect of an embodiment of the present application also provides a terminal, wherein the terminal includes: a memory, a processor, and a topology reconstruction program of a filter coupling matrix stored in the memory and runnable on the processor, wherein the topology reconstruction program of the filter coupling matrix, when executed by the processor, implements the steps of the topology reconstruction method of the filter coupling matrix as described above.

[0032] The fourth aspect of an embodiment of the present application also provides a computer-readable storage medium, wherein the computer-readable storage medium stores a topology reconstruction program of a filter coupling matrix, and when the topology reconstruction program of the filter coupling matrix is ​​executed by a processor, the steps of the topology reconstruction method of the filter coupling matrix as described above are implemented.

[0033] Beneficial effects: The present application provides a topological reconstruction method, system, terminal and medium for a filter coupling matrix. The present application targets frequency-varying coupling in a target topology. By performing singular value decomposition and Gaussian elimination on the transformation matrix, a predetermined reconstruction path is obtained analytically. The reconstruction path is applicable to other responses under the same target, and is combined with the objective function and the derived analytical gradient to improve the computational efficiency of the target coupling matrix containing frequency-varying coupling in the target topology. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are only some embodiments recorded in this application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0035] Figure 1 It is a flow chart of a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0036] Figure 2 This is a flowchart of specific implementation steps of the entire execution process in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0037] Figure 3 It is an eighth-order extended box-type topology structure and a random coupling matrix in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0038] Figure 4 This is a schematic diagram of an eight-level expansion box topology reconstruction path in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0039] Figure 5 This is a comparison between an eighth-order extended box topology coupling matrix and an eighth-order extended box response in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0040] Figure 6 This is an eighth-order extended box topology coupling matrix and response comparison after parameter modification in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0041] Figure 7 It is a fifth-order comprehensive example contract transformation matrix in a preferred embodiment of the topological reconstruction method of the filter coupling matrix of the present application;

[0042] Figure 8 It is a fifth-order comprehensive example contract transformation matrix in a preferred embodiment of the topological reconstruction method of the filter coupling matrix of the present application;

[0043] Figure 9 This is a schematic diagram of a reconstruction path of a fifth-order topology in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0044] Figure 10 This is a fifth-order topological target coupling matrix and response comparison in a preferred embodiment of the topological reconstruction method of the filter coupling matrix of the present application;

[0045] Figure 11 This is a fifth-order topological target coupling matrix and response comparison after parameter modification in a preferred embodiment of the topological reconstruction method of the filter coupling matrix of the present application;

[0046] Figure 12 It is a seventh-order target topology and a random target topology coupling matrix with non-resonant nodes in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application;

[0047] Figure 13 This is a comparison diagram of a seventh-order comprehensive example response in a preferred embodiment of the topology reconstruction method of the filter coupling matrix of the present application and a comparison diagram of a seventh-order comprehensive example response after parameter modification;

[0048] Figure 14 This is a structural diagram of a preferred embodiment of the topology reconstruction system of the filter coupling matrix of the present application;

[0049] Figure 15 This is a structural diagram of a preferred embodiment of the terminal of this application.

[0050] Description of reference numerals:

[0051] 100. Transformation matrix calculation module; 200. Reconstruction path determination module; 300. Analytical gradient derivation module; 400. Target coupling matrix output module. DETAILED DESCRIPTION

[0052] In order to make the purpose, technical solutions and effects of this application clearer and more specific, the technical solutions in the embodiments of this application will be clearly and completely described below in conjunction with the drawings in the embodiments of this application. The described embodiments are only possible technical implementations of this application and are not all possible implementations. Based on the embodiments in this application, those skilled in the art can fully combine the embodiments of this application to obtain other embodiments without creative work, and these embodiments are also within the scope of protection of this application.

[0053] It should be noted that topology reconstruction refers to converting the filter's coupling matrix from one topology (such as a lateral topology) to another target topology (such as a folded topology, a complex topology with frequency-dependent coupling, or non-resonant nodes) through mathematical transformations (such as rotation, scaling, or orthogonal transformations), while maintaining the filter's electrical performance (such as transmission zeros and return loss). The core of this is to redistribute the coupling paths through matrix transformation to adapt to different physical layouts or performance requirements.

[0054] In the related art, it can only process topologies containing only cross-coupling, and cannot process complex topologies containing frequency-variable coupling (coupling strength varies with frequency) and non-resonant nodes (nodes without inherent resonant frequency); it relies on numerical pre-solution, and some parameters need to be pre-solved through numerical optimization (such as gradient descent, genetic algorithm), and it is impossible to directly derive the reconstruction path analytically, resulting in low computational efficiency and dependence of the results on the initial value; the traditional path is only applicable to a single response (such as a specific frequency response), and different responses under the same topology need to recalculate the path, the number of variables is large, and the optimization cost is high. In the present application, it can support complex topology reconstruction and realize topological reconstruction containing frequency-variable coupling and non-resonant nodes; it can analytically solve the reconstruction path, and directly derive the predefined reconstruction path applicable to all responses through random matrix generation and symmetric diagonalization, without the need for numerical pre-solution; it can improve the optimization efficiency, provide the analytical gradient of the objective function, and combine the Levenberg-Marquardt (iterative optimization) algorithm to accelerate convergence and reduce calculation time.

[0055] The reconstruction path of the filter coupling matrix requires that there is only cross-coupling in the target topology and needs to be pre-solved with the help of numerical methods, but it cannot handle the topology reconstruction containing frequency-varying coupling, resulting in low computational efficiency. This application targets the target topology containing frequency-varying coupling, and performs singular value decomposition and Gaussian elimination on the transformation matrix to analytically obtain a predetermined reconstruction path. This reconstruction path is applicable to other responses under the same target, and is combined with the objective function and the derived analytical gradient to improve the computational efficiency of the target coupling matrix containing frequency-varying coupling in the target topology.

[0056] The present application aims at the topological reconstruction of frequency-variable coupling, which can avoid the emergence of non-singular solutions. The present application can realize the topological reconstruction including frequency-variable coupling and non-resonant nodes. First, a random matrix with the target topological structure is generated, and then the transformation matrix is ​​obtained by the simultaneous diagonalization method of the symmetric matrix. Then, the reconstruction path can be analytically predetermined by singular value decomposition and Gaussian elimination. Importantly, this reconstruction path is also applicable to other responses under the same target topology. Therefore, the pre-reconstruction path will greatly reduce the number of variables in the optimization model, thereby saving computing time and cost. In order to speed up the convergence of the optimization, an analytical gradient of the objective function is also provided.

[0057] The following specific embodiments are used to describe the technical solution of the present application in detail. The following specific embodiments can be combined with each other, and the same or similar concepts or processes may not be described in detail in some embodiments.

[0058] The topology reconstruction method of the filter coupling matrix described in the preferred embodiment of the present application is as follows: Figure 1 As shown, the topology reconstruction method of the filter coupling matrix includes the following steps:

[0059] In step S101 , a random coupling matrix and a random capacitance matrix of a target topology are obtained, and a transformation matrix is ​​obtained according to the random coupling matrix and the random capacitance matrix.

[0060] In one possible implementation, based on the random coupling matrix and the random capacitance matrix, a fully diagonalized coupling diagonal matrix and a capacitance diagonal matrix are obtained; based on the coupling diagonal matrix and the capacitance diagonal matrix, a transverse topological coupling matrix and a transverse topological capacitance matrix are obtained; based on the transverse topological coupling matrix and the transverse topological capacitance matrix, a transformation matrix is ​​obtained.

[0061] This application diagonalizes the randomly generated coupling matrix and capacitance matrix through orthogonal transformation, provides a normalized initial topology for subsequent reconstruction path derivation, and eliminates interference from off-diagonal elements.

[0062] Specifically, during the simultaneous diagonalization of the symmetric matrix, the N+2 (N is the filter order) order coupling matrix M under the target topology is first randomly generated. T and the capacitance matrix C T Although M T and C T The response is uncontrollable but still acceptable because M T and C T It is only used to predetermine the reconstruction path. T and C T The form is:

[0063]

[0064] Among them, M T is the coupling matrix under the randomly generated target topology, C T is the capacitance matrix of the randomly generated target topology, T represents the transpose; M0 is an N-order real symmetric matrix, representing the coupling relationship between nodes; C0 is an N-order real symmetric matrix, representing the capacitance relationship between nodes; r S is the coupling vector between the source and the node, r L is the coupling vector between the load and the node, v S is the capacitance vector between the source and the node, v L is the capacitance vector between the load and the node, r SL is the source-load direct coupling vector, v SL is the source-load direct capacitance vector.

[0065] Spectral decomposition of C0 yields:

[0066]

[0067] Among them, C A is the matrix after C0 is orthogonally transformed; Q1 is an orthogonal matrix; C1 is a non-singular diagonal matrix with a rank of p, where p is a constant. diag represents a diagonal matrix operation. The same transformation is performed on M0:

[0068]

[0069] Among them, M A is the matrix after orthogonal transformation of M0; M1 is a p-order matrix, and M3 is an Np-order matrix. Then, perform spectral decomposition on M3:

[0070]

[0071] Where V1 is the corresponding orthogonal matrix, and M6 is a non-singular diagonal matrix. Let Q2 = diag(I p , V1), I pis the p-order identity matrix, and Q2 acts on C A , making Similarly, Q2 is applied to M A :

[0072]

[0073] Where Q2 is the identity matrix I p and the orthogonal matrix V1; C B C A The matrix after Q2 transformation, M B M A The matrix after Q2 transformation; M4 and M5 are the block matrices generated after transformation.

[0074] M5 is usually an empty matrix. If it is neither an empty matrix nor a zero matrix, it indicates that the coupling matrix M T and the capacitance matrix C T It is not possible to diagonalize at the same time. Then, define the orthogonal matrix Q3:

[0075]

[0076] Among them, Q3 is an orthogonal matrix used to eliminate M B The non-diagonal elements in; q = rank (M6), rank is the rank of the matrix, q is the rank of the matrix M6; I N-p-q is the Npq order unit matrix; then the matrix Q3 acts on M B and C B :

[0077]

[0078]

[0079] Among them, C C C B The matrix after Q3 transformation; M C M B The matrix after Q3 transformation.

[0080] Pair Matrix Perform spectral decomposition:

[0081]

[0082] Among them, V2 is a non-singular matrix; λ1, λ t is the eigenvalue. Perform spectral decomposition:

[0083]

[0084] Define the orthogonal matrix Q4 as:

[0085]

[0086] Among them, Q4 is an orthogonal matrix and R is an orthogonal matrix.

[0087] Finally, matrix Q4 is applied to matrix M C and C C , we can get two diagonal matrices:

[0088]

[0089] Among them, M D is the final diagonal matrix, that is, the coupling diagonal matrix; C D is the final diagonal matrix, that is, the capacitance diagonal matrix.

[0090] Define the transformation matrix P in P in =Q1Q2Q3Q4 (combined orthogonal matrix, representing the transformation from the target topology to the lateral topology), and the extended transformation matrix P t (Converting the landscape topology to the target topology) is defined as:

[0091]

[0092] The matrix P t Acting on the matrix M T and C T , we can get the lateral topological coupling matrix:

[0093]

[0094] Among them, M trans is the coupling matrix of the lateral topology, C trans is a capacitor matrix of lateral topology.

[0095] According to the established comprehensive theory, the transformation matrix from the classic topology such as the folded topology to the target topology can be obtained:

[0096] M f =(P t Q f ) T M T P t Q f ; C f =(P t Q f ) T C T P t Q f ;

[0097] Among them, Q f Represents the orthogonal transformation matrix from the horizontal topology to the folded topology, M f is the coupling matrix of the classical topology, C f is the capacitance matrix of the classical topology; finally, the transformation matrix P (used to transform from the classical topology to the target topology) is defined as:

[0098] P=P t Q f .

[0099] The simultaneous diagonalization of symmetric matrices in this application is the cornerstone of topological reconstruction. Through orthogonal transformation, complex topology is normalized into a diagonal form, providing efficient and stable initial conditions for subsequent reconstruction path derivation and optimization.

[0100] In step S102, if the target topology contains frequency-variant coupling, the transformation matrix is ​​subjected to singular value decomposition and rotation matrix decomposition to obtain the product of the scaling matrix and the product of the rotation matrix, and a reconstruction path is obtained based on the product of the scaling matrix and the product of the rotation matrix.

[0101] In a possible implementation, singular value decomposition is performed on the transformation matrix to obtain a singular value diagonal matrix and a rotation matrix; the singular value diagonal matrix is ​​decomposed into a product of scaling matrices; and the rotation matrix is ​​decomposed into a product of rotation matrices.

[0102] Specifically, see Figure 2 , during the transformation matrix decomposition process, if the target topology contains frequency-variant coupling and non-resonant nodes, it is necessary to first perform singular value decomposition:

[0103] P=UDV T ;

[0104] Among them, P is the change matrix; matrices U and V are orthogonal matrices; matrix D is a diagonal matrix containing singular values ​​(scaling factors), which can be decomposed into the product of scaling matrices:

[0105]

[0106] Where N is the filter order, S i is the scaling matrix, and the product of the scaling matrix is ​​expressed as:

[0107] Among them, α i is the scaling factor, which represents the scaling of the i-th dimension.

[0108] This application decomposes complex transformations into primitive operations (rotation and scaling) through singular value decomposition, providing a mathematical form of analyzable operations for subsequent reconstruction path derivation.

[0109] The next goal is to decompose the orthogonal matrix into the product of rotation matrices. Taking the above orthogonal matrix U as an example, Gaussian elimination can be used to gradually reduce the non-diagonal elements to zero:

[0110] U'=R ij U;

[0111] Among them, R ij is the rotation matrix; (i, j) is the rotation center index, indicating the rotation operation on the element in the i-th row and j-th column; the product of the rotation matrices is expressed as:

[0112]

[0113] Among them, R ij is the rotation matrix, (i, j) is the rotation center, θ ij is the rotation angle.

[0114] cosθ ij and sinθ ij They are:

[0115]

[0116] Among them, U ii is the element in the i-th row and i-th column of the matrix U, U ji is the element in the i-th row and j-th column of the U matrix.

[0117] When U ii and U ji When both are zero, the rotation angle is 0°. Repeating the above process can convert the orthogonal matrix into the identity matrix:

[0118]

[0119] By multiplying both sides of the above equation by the inverse matrix of the rotation matrix and excluding the rotation center whose rotation angle is an integer multiple of 180°, the U matrix can be expressed as:

[0120]

[0121] Where m represents the remaining rotation center, R m is the remaining rotation transformation, n is the number of rotation transformations performed, which satisfies the following relationship:

[0122]

[0123] N is the filter order.

[0124] This application converts the orthogonal matrix into the identity matrix through continuous rotation operations, so that U is expressed as the product of the rotation matrices.

[0125] The reconstruction path from the classic topology to the target topology can be derived through the above method;

[0126] When the target topology includes frequency-variable coupling and non-resonant nodes, the reconstruction path is expressed as:

[0127]

[0128] Among them, M T is the target topological coupling matrix, R i (θ i ) is the rotation angle θ i The rotation matrix acting on one side, R j (θ j ) is the rotation angle θ j The rotation matrix acting on the other side; S l (α l ) is the scaling factor α l The scaling matrix R i and R j are the rotation matrices decomposed from matrices U and V, S l is the scaling matrix decomposed from the diagonal matrix; x and z are the number of rotation transformations, y is the number of scaling transformations, and M f is the classical topological coupling matrix, C T is the target topology capacitance matrix, C f is the classical topological capacitance matrix, and T represents the transpose.

[0129] At this point, the reconstruction path of any target topology can be derived through the above method. The next step is to establish the objective function and solve the corresponding rotation angle.

[0130] This application uses singular value decomposition and Gaussian elimination to parse complex transformations into primitive operations (rotation and scaling) and derive a universal reconstruction path. The rotation operation adjusts the phase relationship of the coupling path to eliminate redundant coupling; the scaling operation adjusts the coupling strength to match the response characteristics of the target topology. The pre-derived reconstruction path is applicable to different responses under the same target topology, requiring only adjustments to the rotation angle and scaling factor.

[0131] In another possible implementation, if the target topology does not contain frequency-variant coupling, rotation matrix decomposition is performed on the transformation matrix to obtain a product of rotation matrices, and a reconstruction path is obtained according to the product of the rotation matrices.

[0132] Specifically, when the topology does not include frequency-variable coupling and non-resonant nodes, the reconstruction path is expressed as:

[0133]

[0134] Among them, n is the number of rotation transformations, R m (θ m ) is the mth rotation angle θ m The rotation transformation, M f is the classical topological coupling matrix, M T is the target topology coupling matrix.

[0135] For different responses under the same target topology, the reconstruction path does not change. Therefore, only the corresponding rotation angle needs to be solved.

[0136] In step S103, an objective function is established, and gradient derivation is performed based on the objective function and the reconstruction path to obtain an analytical gradient.

[0137] In one possible implementation, the non-diagonal elements of the target topological coupling matrix and the target topological capacitance matrix are simultaneously constrained to be zero to obtain an objective function; and the analytical gradient of the objective function with respect to the rotation angle and the scaling factor is derived according to the reconstruction path.

[0138] This application uses the chain rule to explicitly derive the gradient of the objective function with respect to the rotation angle and scaling factor, avoiding numerical differential errors and significantly improving the optimization convergence speed. The rotation gradient guides the adjustment of the phase relationship of the coupling path to eliminate redundant coupling; the scaling gradient guides the adjustment of the coupling strength to match the response characteristics of the target topology. The pre-derived gradient formula is applicable to different responses under the same target topology, requiring only parameter adjustments.

[0139] Specifically, in the analytical gradient derivation process, if the target topology contains frequency-variable coupling and non-resonant nodes. When the topology contains frequency-variable coupling and non-resonant nodes, the loss function is modified to, that is, the objective function is expressed as:

[0140] M T (i,j)=0,when(i,j)∈T M ;

[0141] C T (i,j)=0,when(i,j)∈T C ;

[0142] Among them, M T is the target topological coupling matrix, (i, j) is the rotation center index acting on the (i, j)th row and jth column, T M is the node index of the element that should be 0 in the target topology coupling matrix, C T is the target topology capacitance matrix, T C The node indices of the elements in the target capacitance matrix that should be 0.

[0143] To obtain the normalized target capacitance matrix C T, an additional normalization operation will be performed after solving. The analytical gradient includes the objective function with respect to the rotation angle θ i The analytical gradient and the scaling factor α l The analytical gradient of the objective function with respect to the rotation angle θ i The analytical gradient is modified to:

[0144]

[0145] in, is the objective function M T About the rotation angle θ i The partial derivative of R k is the rotation matrix acting on the kth rotation operation, is the rotation matrix R i About the rotation angle θ i The derivative of R j is the rotation matrix acting on the jth rotation operation, M f is the classical topological coupling matrix, S l is the scaling matrix acting on the lth one, x and z are the number of rotation transformations, y is the number of scaling transformations, C f is a classical topological capacitor matrix;

[0146] The loss function is about the scaling factor α l The gradient of is:

[0147]

[0148] in, is the objective function M T About the scaling factor α l The partial derivative of α l is the lth scaling factor, R i is the rotation matrix acting on the i-th rotation operation, is the scaling matrix S l About the scaling factor α l The derivative of , T represents the transpose.

[0149]

[0150] Other analytical gradients are similar to those described above and will not be described in detail. In order to minimize the objective function, this application uses the Levenberg-Marquardt algorithm.

[0151] In another possible implementation, the target topology does not contain frequency-dependent coupling and non-resonant nodes. The objective function is given in the form of a nonlinear system of equations:

[0152] M T(i,j)=0,when(i,j)∈T M ;

[0153] Among them, T M Represents the target coupling matrix M T The node index of the element that should be 0, i represents the row, and j represents the column. To accelerate the convergence of the algorithm, the analytical gradient of the objective function is:

[0154]

[0155] in, yes The element in the i-th row and j-th column of for:

[0156]

[0157] The microwave filter topology reconstruction strategy of the present application can complete topology reconstruction including cross-coupling, frequency-variant coupling and non-resonant nodes; the reconstruction path is solved analytically using a randomly generated target coupling matrix without the need for other numerical methods; the transformation matrix is ​​decomposed using singular value decomposition and Gaussian elimination to obtain the reconstruction path; and the analytical gradient of the objective function is given to improve the efficiency of the algorithm.

[0158] In step S104, the transformation parameters are adjusted according to the analytical gradient and the objective function to obtain a target topological coupling matrix.

[0159] Specifically, during the iterative optimization process, the initial rotation angle and scaling factor are randomly generated; the objective function value is calculated according to the current parameters; the analytical gradient is calculated using the derived gradient formula; the parameters are updated according to the Levenberg-Marquardt algorithm; and if the convergence condition is that the objective function value is less than the preset threshold, or the parameter update amount is less than the tolerance, the optimized parameters and the corresponding target coupling matrix and capacitance matrix are output.

[0160] The present application can realize topology reconstruction including cross-coupling, frequency-variant coupling and non-resonant nodes. First, the coupling matrix and capacitance matrix under the target topology are randomly initialized. Then, through the simultaneous diagonalization algorithm of symmetric matrices, the transformation matrix that reconstructs the initial coupling matrix and capacitance matrix into any classical topology can be solved. Afterwards, the transformation matrix is ​​decomposed by singular value decomposition and Gaussian elimination, and the reconstruction path of this process can be directly determined. Most importantly, the reconstruction path is only related to the target topology, but not to the transmission zero point position and return loss. With the help of the predetermined reconstruction path, a more efficient optimization model can be established to accelerate the synthesis of the target topology with a satisfactory response. In addition, in order to further improve the optimization efficiency, the analytical gradient of the objective function is given. The effectiveness of the proposed synthesis framework is verified through multiple examples.

[0161] The topology reconstruction method of the filter coupling matrix of the present application is further described below through specific embodiments.

[0162] Example 1, see Figure 3 , eighth-order expanded box topology:

[0163] It was first applied to the synthesis of the eighth-order extended box topology, with the filter parameters of return loss 20dB and transmission zero position [-1.8, -1.2, 1.5]. The target topology and initial random matrix are as follows Figure 3 As shown, through the simultaneous diagonalization algorithm of the symmetric matrix and the Gaussian elimination method, the orthogonal transformation matrix P and the reconstruction path from the folding type to the target topology can be derived. The orthogonal transformation matrix and reconstruction path of the eight-level synthesis example are shown in the following formula:

[0164]

[0165] R 24 R 34 R 35 R 45 R 46 R 47 R 56 R 57 R 67 ·M f ·(R 24 R 34 R 35 R 45 R 46 R 47 R 56 R 57 R 67 ) T =M T ;

[0166] The subscripts in the above formulas represent the rotation centers corresponding to the nodes. Figure 4 To reconstruct the path diagram, the topology matrix of the target topology and the eight-level expanded box topology matrix are shown in the following formula:

[0167]

[0168] According to the proposed method, the loss function is established and the corresponding rotation angle is solved. The solution of the rotation angle is: (52.17 ° ,-93.50 ° ,25.24 ° ,-130.31 ° ,-29.94 ° ,-36.41 ° ,333.44 °,-24.75 ° ,-39.94 ° ), the coupling matrix and response are solved as Figure 5 The derived reconstruction path is also applicable to other responses under this topology. The filter parameters are modified to return loss 22dB and the transmission zero position is [-2.6, -2, -1.2]. The corresponding rotation angle is (-63.50 ° ,-113.42 ° ,-46.67 ° ,28.40 ° ,199.90 ° ,-28.46 ° ,179.68 ° ,-0.42 ° ,127.22 ° ); Figure 6 Shown are the solved coupling matrices and responses, Figure 6 (a) is the eighth-order extended box topology coupling matrix after the parameters are modified. Figure 6 (b) is the response comparison of the eighth-order extended box topology after parameter modification.

[0169] Example 2, see Figure 7 , including a fifth-order topology with frequency-dependent coupling:

[0170] In order to verify that the proposed method can synthesize frequency-variable coupling topology, a fifth-order synthesis example is given, whose return loss and transmission zero are 20dB and [-1.7,-1.3,2.1]. Figure 7 is the target topology and the initial random coupling matrix. It should be noted that the capacitance matrix only needs to give off-diagonal random values, where CT(2,3)=CT(3,2)=-0.6019. According to the simultaneous diagonalization method of symmetric matrices introduced, the contract transformation matrix from the folded type to the target topology can be obtained, as shown in Figure 8 shown.

[0171] The contract transformation matrix can be decomposed into the product of the rotation matrix and the scaling matrix, that is, the reconstruction path:

[0172]

[0173] Among them, R ' 23 Represents the rotation matrix decomposed from the matrix V, which is the same as R 23 have the same center of rotation and different angles of rotation. Figure 9 Schematic diagram of the reconstruction path.

[0174] The topological matrix of the coupling matrix and the capacitance matrix, the topological matrix of the fifth-order synthesis example is shown in the following formula:

[0175]

[0176] Construct the objective function and solve the rotation angle. The coupling matrix and response are as follows: Figure 10 As shown. Modify the filter parameters, the reconstruction path is still applicable, the return loss and transmission zero are modified to return loss 18dB, transmission zero [-1.8, -1.3, 2], the coupling matrix and rotation angle are solved as follows Figure 11 and as shown in Table 1.

[0177] Table 1: Synthesis solution of fifth-order synthesis example

[0178]

[0179] Example 3, see Figure 12 , a seventh-order topology including non-resonant nodes:

[0180] A seventh-order synthesis example with a non-resonant node is given, where the return loss and transmission zero are return loss 20dB and transmission zeros [-1.68, 1.31, 1.79]. Figure 12 is the target topology and the initial random coupling matrix. According to the SMSD method, the contract transformation matrix from the folded type to the target topology can be obtained. The contract transformation matrix of the seventh-order synthesis example is shown in the following formula:

[0181]

[0182] The reconstruction path can be derived by simultaneous diagonalization of symmetric matrices and Gaussian elimination:

[0183] UDV T M f (UDV T ) T =M T ;

[0184] in,

[0185] U=R 23 R 24 R 26 R 27 R 34 R 35 R 36 R 45 R 46 R 56 R 57 ;

[0186] D = S3S4S5S6;

[0187]

[0188] Establish the objective function and solve it, the response is as follows Figure 13 As shown in (a) in the figure. Modify the return loss and transmission zero parameters to return loss 25dB and transmission zero [-1.5, -1.2, 1.7], the reconstructed path remains unchanged, and the response is as follows Figure 13 Table 2 shows the coupling matrix corresponding to the two responses.

[0189] Table 2: Target coupling matrix for seventh-order synthesis example

[0190]

[0191]

[0192] Next, a topology reconstruction system for a filter coupling matrix proposed in an embodiment of the present application will be described with reference to the accompanying drawings.

[0193] Figure 14 It is a structural diagram of the topology reconstruction system of the filter coupling matrix of an embodiment of the present application.

[0194] like Figure 14 As shown, the topology reconstruction system of the filter coupling matrix includes: a transformation matrix calculation module 100, a reconstruction path determination module 200, an analytical gradient derivation module 300 and a target coupling matrix output module 400.

[0195] Specifically, the transformation matrix calculation module 100 is used to obtain a random coupling matrix and a random capacitance matrix of a target topology, and obtain a transformation matrix according to the random coupling matrix and the random capacitance matrix;

[0196] A reconstruction path determination module 200 is configured to, if the target topology contains frequency-variant coupling, perform singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain the product of a scaling matrix and a rotation matrix, and obtain a reconstruction path based on the product of the scaling matrix and the rotation matrix;

[0197] An analytical gradient derivation module 300 is used to establish an objective function and perform gradient derivation based on the objective function and the reconstruction path to obtain an analytical gradient;

[0198] The target coupling matrix output module 400 is used to adjust the transformation parameters according to the analytical gradient and the objective function to obtain a target topological coupling matrix.

[0199] Figure 15 This is a diagram of the structure of a terminal provided in an embodiment of the present application. The terminal may include:

[0200] Memory 501 , processor 502 , and computer programs stored in the memory 501 and executable on the processor 502 .

[0201] When the processor 502 executes the program, the topology reconstruction method of the filter coupling matrix provided in the above embodiment is implemented.

[0202] Furthermore, the terminal further includes:

[0203] The communication interface 503 is used for communication between the memory 501 and the processor 502 .

[0204] The memory 501 is used to store computer programs that can be run on the processor 502 .

[0205] The memory 501 may include a high-speed RAM memory, and may also include a non-volatile memory (non-volatile memory), such as at least one disk memory.

[0206] If the memory 501, processor 502, and communication interface 503 are implemented independently, the communication interface 503, memory 501, and processor 502 can be connected to each other via a bus and communicate with each other. The bus can be an Industry Standard Architecture (ISA) bus, a Peripheral Component Interconnect (PCI) bus, or an Extended Industry Standard Architecture (EIS) bus. The bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, Figure 15 Only one thick line is used in the diagram, but this does not mean that there is only one bus or one type of bus.

[0207] Optionally, in a specific implementation, if the memory 501, the processor 502 and the communication interface 503 are integrated on a chip, the memory 501, the processor 502 and the communication interface 503 can communicate with each other through an internal interface.

[0208] The processor 502 may be a central processing unit (CPU), an application specific integrated circuit (ASIC), or one or more integrated circuits configured to implement the embodiments of the present application.

[0209] This embodiment further provides a computer-readable storage medium having a computer program stored thereon. When the program is executed by a processor, the above-mentioned topology reconstruction method of the filter coupling matrix is ​​implemented.

[0210] One embodiment of the present application provides a computer program product, including a computer program, which, when executed by a processor, implements the Figure 1 A topology reconstruction method for a filter coupling matrix provided in any of the corresponding embodiments.

[0211] Any process or method description in a flowchart or otherwise described herein may be understood to represent a module, fragment or portion of code comprising one or N executable instructions for implementing a custom logical function or process step, and the scope of the preferred embodiments of the present application includes alternative implementations in which functions may be performed in a different order than shown or discussed, including performing functions in a substantially simultaneous manner or in a reverse order depending on the functions involved, which should be understood by those skilled in the art to which the embodiments of the present application pertain.

[0212] The logic and / or steps represented in the flowcharts or otherwise described herein, for example, can be considered as a sequenced list of executable instructions for implementing the logical functions, and can be embodied in any computer-readable storage medium for use by, or in conjunction with, an instruction execution system, apparatus, or device (e.g., a computer-based system, a system including a processor, or other system that can fetch and execute instructions from an instruction execution system, apparatus, or device). For purposes of this specification, a "computer-readable storage medium" can be any device that can contain, store, communicate, propagate, or transport a program for use by, or in conjunction with, an instruction execution system, apparatus, or device. More specific examples (a non-exhaustive list) of computer-readable storage media include the following: an electrical connection having one or N wires (electronic devices), a portable computer disk cartridge (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and programmable read-only memory (EPROM or flash memory), a fiber optic device, and a portable compact disc read-only memory (CDROM). In addition, the computer-readable storage medium may even be paper or other suitable medium on which the program is printed, since the program can be obtained electronically by optically scanning the paper or other medium and then editing, interpreting or processing it in other suitable ways as necessary, and then storing it in a computer memory.

[0213] It should be understood that various parts of the present application can be implemented using hardware, software, firmware, or a combination thereof. In the above embodiment, the N steps or methods can be implemented using software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented using hardware, as in another embodiment, any one of the following technologies known in the art or a combination thereof can be used to implement: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, an application-specific integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0214] Those skilled in the art will understand that all or part of the steps in the method of the above embodiment can be completed by instructing related hardware through a program, and the program can be stored in a computer-readable storage medium. When the program is executed, it includes one or a combination of the steps of the method embodiment.

[0215] In addition, the functional units in the various embodiments of the present application may be integrated into a processing module, or each unit may exist physically separately, or two or more units may be integrated into a module. The above-mentioned integrated module may be implemented in the form of hardware or in the form of a software functional module. If the integrated module is implemented in the form of a software functional module and sold or used as an independent product, it may also be stored in a computer-readable storage medium.

[0216] The storage medium mentioned above may be a read-only memory, a magnetic disk, or an optical disk, etc. Although the embodiments of the present application have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present application. Persons skilled in the art may make changes, modifications, substitutions, and variations to the above embodiments within the scope of the present application.

[0217] It should be understood that the application of this application is not limited to the above examples. For ordinary technicians in this field, they can make improvements or changes based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to this application.

[0218] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present application, rather than to limit them. Although the present application has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some or all of the technical features therein. These modifications or replacements do not deviate the essence of the corresponding technical solutions from the scope of the technical solutions of the embodiments of the present application.

Claims

1. A topology reconstruction method for a filter coupling matrix, characterized in that: The topology reconstruction method of the filter coupling matrix includes: Obtaining a random coupling matrix and a random capacitance matrix of a target topology, and obtaining a transformation matrix according to the random coupling matrix and the random capacitance matrix; If the target topology contains frequency-variant coupling, performing singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain a product of a scaling matrix and a product of a rotation matrix, and obtaining a reconstruction path according to the product of the scaling matrix and the product of the rotation matrix; Establishing an objective function, and performing gradient derivation based on the objective function and the reconstruction path to obtain an analytical gradient; The transformation parameters are adjusted according to the analytical gradient and the objective function to obtain a target topological coupling matrix.

2. The topology reconstruction method of the filter coupling matrix according to claim 1, characterized in that: Obtaining a transformation matrix according to the random coupling matrix and the random capacitance matrix specifically includes: According to the random coupling matrix and the random capacitance matrix, a completely diagonalized coupling diagonal matrix and a capacitance diagonal matrix are obtained; Obtaining a transverse topological coupling matrix and a transverse topological capacitance matrix according to the coupling diagonal matrix and the capacitance diagonal matrix; A transformation matrix is ​​obtained according to the transverse topological coupling matrix and the transverse topological capacitance matrix.

3. The topology reconstruction method of the filter coupling matrix according to claim 1, characterized in that: The step of obtaining a transformation matrix according to the random coupling matrix and the random capacitance matrix further includes: If the target topology does not contain frequency-variant coupling, performing rotation matrix decomposition on the transformation matrix to obtain a product of rotation matrices, and obtaining a reconstruction path according to the product of the rotation matrices; The reconstruction path is expressed as: Among them, n is the number of rotation transformations, R m (θ m ) is the mth rotation angle θ m The rotation transformation, M f is the classical topological coupling matrix, M T is the target topology coupling matrix.

4. The topology reconstruction method of the filter coupling matrix according to claim 1, characterized in that: The step of performing singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain the product of a scaling matrix and a rotation matrix specifically includes: Performing singular value decomposition on the transformation matrix to obtain a singular value diagonal matrix and a rotation matrix; The singular value diagonal matrix is ​​decomposed into the product of scaling matrices, which is expressed as: Among them, S i is the scaling matrix, α i is the scaling factor; The rotation matrix is ​​decomposed into the product of rotation matrices, which is expressed as: Among them, R ij is the rotation matrix, (i, j) is the rotation center, θ ij is the rotation angle.

5. The topology reconstruction method of the filter coupling matrix according to claim 4, characterized in that: The reconstruction path is expressed as: Among them, M T is the target topological coupling matrix, R i (θ i ) is the rotation angle θ i The rotation matrix acting on one side, R j (θ j ) is the rotation angle θ j The rotation matrix acting on the other side, S l (α l ) is the scaling factor α l The scaling matrix, x and z are the number of rotation transformations, y is the number of scaling transformations, M f is the classical topological coupling matrix, C T is the target topology capacitance matrix, C f is the classical topological capacitance matrix, and T represents the transpose.

6. The topology reconstruction method of the filter coupling matrix according to claim 4, characterized in that: The establishing of the objective function and performing gradient derivation based on the objective function and the reconstruction path to obtain an analytical gradient specifically includes: Simultaneously constraining the non-diagonal elements of the target topology coupling matrix and the target topology capacitance matrix to be zero, thereby obtaining an objective function; According to the reconstruction path, the analytical gradient of the objective function with respect to the rotation angle and the scaling factor is derived.

7. The topology reconstruction method of the filter coupling matrix according to claim 6, characterized in that: The objective function is expressed as: M T (i,j)=0,when(i,j)∈T M ; C T (i,j)=0,when(i,j)∈T C ; Among them, M T is the target topological coupling matrix, (i, j) is the rotation center index acting on the (i, j)th row and jth column, T M is the node index of the element that should be 0 in the target topology coupling matrix, C T is the target topology capacitance matrix, T C is the node index of the element that should be 0 in the target capacitance matrix; The analytical gradient is expressed as: in, is the objective function M T About the rotation angle θ i The partial derivative of R k is the rotation matrix acting on the kth rotation operation, is the rotation matrix R i About the rotation angle θ i The derivative of R j is the rotation matrix acting on the jth rotation operation, M f is the classical topological coupling matrix, S l is the scaling matrix acting on the lth one, x and z are the number of rotation transformations, y is the number of scaling transformations, C f is a classical topological capacitor matrix; is the objective function M T About the scaling factor α l The partial derivative of α l is the lth scaling factor, R i is the rotation matrix acting on the i-th rotation operation, is the scaling matrix S l About the scaling factor α l The derivative of , T represents the transpose.

8. A topology reconstruction system for a filter coupling matrix, characterized in that: The topology reconstruction system of the filter coupling matrix includes: a transformation matrix calculation module, configured to obtain a random coupling matrix and a random capacitance matrix of a target topology, and obtain a transformation matrix according to the random coupling matrix and the random capacitance matrix; a reconstruction path determination module, configured to, if the target topology contains frequency-variant coupling, perform singular value decomposition and rotation matrix decomposition on the transformation matrix to obtain a product of a scaling matrix and a product of a rotation matrix, and obtain a reconstruction path based on the product of the scaling matrix and the product of the rotation matrix; An analytical gradient derivation module is used to establish an objective function and perform gradient derivation based on the objective function and the reconstruction path to obtain an analytical gradient; The target coupling matrix output module is used to adjust the transformation parameters according to the analytical gradient and the objective function to obtain the target topological coupling matrix.

9. A terminal, characterized in that: The terminal includes: a memory, a processor, and a topology reconstruction program of a filter coupling matrix stored in the memory and runnable on the processor. When the topology reconstruction program of the filter coupling matrix is ​​executed by the processor, the steps of the topology reconstruction method of the filter coupling matrix as described in any one of claims 1 to 7 are implemented.

10. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a topology reconstruction program for a filter coupling matrix, and when the topology reconstruction program for the filter coupling matrix is ​​executed by a processor, the steps of the topology reconstruction method for the filter coupling matrix according to any one of claims 1 to 7 are implemented.

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