CN110866356A - Filter coupling matrix decoupling transformation method based on hybrid optimization algorithm - Google Patents
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Abstract
The invention discloses a filter coupling matrix decoupling transformation method based on a hybrid optimization algorithm, which is characterized by comprising the following steps of: step S1, obtaining a hybrid optimization initial matrix M through a synthesis method and rotation eliminatione(ii) a Step S2, optimizing the initial matrix M based on mixingePerforming decoupling transformation in the global optimization stage according to the optimization constraint conditions and the optimization fitness index to obtain a global optimization matrix Md(ii) a Step S3, the global optimization matrix M is processed by gradient algorithmdThe matrix elements are locally optimized, and a final decoupling transformation matrix M is output0. The decoupling transformation method of the filter coupling matrix based on the hybrid optimization algorithm has good applicability to the decoupling transformation of the filter coupling matrix, so that the coupling matrix optimally solved can accurately approach the actual characteristics of the filter.
Description
Technical Field
The invention relates to the technical field of modeling simulation of radio frequency microwave filters, in particular to a decoupling transformation method of a filter coupling matrix based on a hybrid optimization algorithm.
Background
In the theoretical research and design of microwave filters, the design process based on the synthesis method is realized by extracting a response curve to establish a coupling matrix and combining the filter design, the matrix is simplified by a matrix similarity transformation method to obtain a matrix decoupling form matched with a topological structure, particularly for a filter with a higher order, a direct coupling matrix needs to be transformed into a folding matrix by a rotation element elimination method, and the coupling matrix decoupling forms matched with filters with different topological structures can be obtained by multiplying elements at different positions of the rotation matrix and the coupling matrix according to a certain sequence.
However, since the actual engineering structure has cross coupling in different topological forms, on one hand, a coupling matrix satisfying all topological forms cannot be obtained by adopting a common element elimination method, and some actual structures cannot be directly obtained through matrix similarity transformation; secondly, the response of the transformed coupling matrix is greatly different from the response of the final physical structure, so that the initial value given by the coupling matrix is not accurate when the filter is optimized, and the time consumption is long because commercial electromagnetic FFA (finite element analysis) software is further used for multiple simulation optimization.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: aiming at the problems that a common element elimination method is difficult to generally apply due to different decoupling conversion methods of different coupling matrixes of filter topology and the difference between a converted matrix and a final physical structure is large, the decoupling conversion method of the coupling matrix of the filter based on the hybrid optimization algorithm is provided.
The technical scheme adopted by the invention is as follows:
a decoupling transformation method of a filter coupling matrix based on a hybrid optimization algorithm comprises the following steps:
step S1, obtaining a hybrid optimization initial matrix M through a synthesis method and rotation eliminatione；
Step S2, optimizing the initial matrix M based on mixingePerforming decoupling transformation in the global optimization stage according to the optimization constraint conditions and the optimization fitness index to obtain a global optimization matrix Md；
Step S3, the global optimization matrix M is processed by gradient algorithmdThe matrix elements are locally optimized, and a final decoupling transformation matrix M is output0。
Further, step S1 is specifically:
(1) obtaining a coupling matrix M by adopting a filter coupling matrix synthesis method;
(2) performing rotation elimination on the coupling matrix M by multiplying the rotation matrix by multiple iterations, and taking the matrix after the rotation elimination as a hybrid optimization initial matrix Me。
Further, step S2 is specifically:
(1) hybrid optimization initial matrix M according to global optimization algorithm characteristicseCarrying out global optimization to obtain an initialization matrix M'dEncoding the matrix elements in the global optimization, and encoding the matrix elements into optimization parameters according to the selected global optimization algorithm; the optimization constraint conditions comprise that global optimization needs to be initialized randomly according to a certain positive and negative range of an initial value according to the coupling condition and the topological structure of the filter, and the size relation or the symmetrical relation needs to be kept in the whole optimization process of elements with the size relation or the symmetrical relation.
(2) Defining a global optimization fitness index e _ obj:
e_obj＝(Siid-Siie)2；
wherein S isiidRepresenting a decoupled transform matrix MdReflection coefficient S of11Or S22；SiieRepresenting a hybrid-optimized initial matrix MeReflection coefficient S of11Or S22；
(3) Utilizing the global optimization fitness index e _ obj to adopt a global optimization algorithm to initialize a matrix M'dCarrying out iterative adjustment until the optimization result meets the precision requirement, and obtaining a global optimization matrix Md。
Further, the conversion calculation formula of the coupling matrix M-scattering parameter matrix S is:
Sii＝1+2jR1[Z-1]ii；
where Z ═ ω U-jR + M, ω is the normalized frequency, U is the unit matrix of the same order as the coupling matrix M, R is the zero matrix of the same order as the coupling matrix M, except for 1 row and 1 column of elements R in R, N rows and 1 column11＝R1，RN1＝RN，RNIs the normalized source load impedance.
Further, step 3 specifically comprises:
step 3.1, calculate the derivative J of the matrix elements in the local optimizationkl；
Step 3.2, according to the derivative J of the matrix elementklCalculating an iteration step hkl：
Step 3.3, using e _ obj as a local optimization convergence index according to the iteration step length hklPerforming iteration adjustment of local optimization, finishing iteration when the requirement of solving precision is met, and outputting a final decoupling transformation matrix M0。
Further, step 3.1 specifically comprises:
(1) adopting the global optimization fitness index e _ obj in the step 2 as a gradient optimization objective function;
(2) with S11For optimizing the target, respectively deriving each element in the coupling matrix M by using a gradient optimization objective function and a conversion calculation formula of the coupling matrix M-scattering parameter matrix S to obtain a derivative J of each elementkl。
Further, for the matrix elements with the primary and secondary symmetry relationship, the derivative of any one element is shared.
Further, the iteration step is shared by the matrix elements with the primary and secondary symmetry relations.
Further, in step 3.2, the iteration step h is takenklThe real part of the calculation of (2) is taken as the iteration step.
Further, the transformation matrix M is finally decoupled0The following decoupling transformation conditions must be simultaneously satisfied:
1) eigenvalues and eigenvectors, or calculated scattering parameters and hybrid optimization initial matrix MeAn approximation of;
2) the non-zero element positions correspond to the actual filter structure;
3) the coupling condition and the size rule reflected by the matrix elements need to be consistent with the size relation of the actual filter.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that:
the decoupling transformation method of the filter coupling matrix based on the hybrid optimization algorithm has good applicability to the decoupling transformation of the filter coupling matrix, so that the coupling matrix optimally solved can accurately approach the actual characteristics of the filter.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings needed to be used in the embodiments will be briefly described below, it should be understood that the following drawings only illustrate some embodiments of the present invention and therefore should not be considered as limiting the scope, and for those skilled in the art, other related drawings can be obtained according to the drawings without inventive efforts.
Fig. 1 is a flow chart of a filter coupling matrix decoupling transformation method based on a hybrid optimization algorithm according to the present invention.
Fig. 2 is a schematic structural diagram of a fifth-order microstrip direct coupling filter simulated in embodiment 1 of the present invention.
Fig. 3 is a matrix form of a coupling matrix global optimization initialization matrix of a fifth-order microstrip direct-coupling filter according to embodiment 1 of the present invention.
FIG. 4 shows the optimized reflection coefficient S of the coupling matrix in embodiment 1 of the present invention22Compare the figures.
FIG. 5 shows the coupling matrix optimized insertion loss S according to embodiment 1 of the present invention21Compare the figures.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the detailed description and specific examples, while indicating the preferred embodiment of the invention, are intended for purposes of illustration only and are not intended to limit the scope of the invention. The components of embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations. Thus, the following detailed description of the embodiments of the present invention, presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments of the present invention without making any creative effort, shall fall within the protection scope of the present invention.
The invention discloses a decoupling transformation method of a filter coupling matrix based on a hybrid optimization algorithm, which comprises the following steps of:
step S1, obtaining a hybrid optimization initial matrix M through a synthesis method and rotation eliminatione：
(1) Obtaining a coupling matrix M by adopting a filter coupling matrix synthesis method;
(2) performing rotation elimination on the coupling matrix M by multiplying the rotation matrix by multiple iterations, and taking the matrix after the rotation elimination as a hybrid optimization initial matrix Me. The selection of the rotary elimination point, namely the elimination order is related to the represented filter topology, and the subsequent steps of the method are also applicable to matrix structures obtained by different elimination orders.
Step S2, optimizing the initial matrix M based on mixingePerforming decoupling transformation in the global optimization stage according to the optimization constraint conditions and the optimization fitness index to obtain a global optimization matrix Md：
(1) Hybrid optimization initial matrix M according to global optimization algorithm characteristicseCarrying out global optimization to obtain an initialization matrix M'dEncoding the matrix elements in the global optimization, and encoding the matrix elements into optimization parameters according to the selected global optimization algorithm; the optimization constraint conditions comprise that global optimization needs to be initialized randomly according to a certain positive and negative range of an initial value according to the coupling condition and the topological structure of the filter, and the size relation or the symmetrical relation needs to be kept in the whole optimization process of elements with the size relation or the symmetrical relation.
(2) Defining a global optimization fitness index e _ obj:
e_obj＝(Siid-Siie)2；
wherein S isiidRepresenting a decoupled transform matrix MdReflection coefficient S of11Or S22；SiieRepresenting a hybrid-optimized initial matrix MeReflection coefficient S of11Or S22。
Further, the conversion calculation formula of the coupling matrix M-scattering parameter matrix S is:
Sii＝1+2jR1[Z-1]ii；
where Z ═ ω U-jR + M, ω is the normalized frequency, U is the unit matrix of the same order as the coupling matrix M, R is the zero matrix of the same order as the coupling matrix M, except for 1 row and 1 column of elements R in R, N rows and 1 column11＝R1，RN1＝RN，RNIs the normalized source load impedance.
(3) Utilizing the global optimization fitness index e _ obj to adopt a global optimization algorithm to initialize a matrix M'dCarrying out iterative adjustment until the optimization result meets the precision requirement, and obtaining a global optimization matrix Md。
Step S3, adopting gradient algorithm to obtain the global optimization matrix MdThe matrix elements are locally optimized, and a final decoupling transformation matrix M is output0：
Step 3.1, calculating the derivative of the matrix element in the local optimization:
(1) adopting the global optimization fitness index e _ obj in the step 2 as a gradient optimization objective function;
(2) with S11For optimizing the target, respectively deriving each element in the coupling matrix M by using a gradient optimization objective function and a conversion calculation formula of the coupling matrix M-scattering parameter matrix S to obtain a derivative J of each elementkl。
Further, for the matrix elements with the primary and secondary symmetry relationship, the derivative of any one element is shared.
Step 3.2, defining iteration step length h of matrix elements in gradient algorithmkl：
It should be noted that, since each element in the coupling matrix M is a real number, it needs to be iteratedStep length hklThe real part of the calculation of (2) is taken as the iteration step.
Further, the iteration step is shared by the matrix elements with the primary and secondary symmetry relations.
Step 3.3, using e _ obj as a local optimization convergence index according to the iteration step length hklPerforming iteration adjustment of local optimization, finishing iteration when the requirement of solving precision is met, and outputting a final decoupling transformation matrix M0。
Further, the transformation matrix M is finally decoupled0The following decoupling transformation conditions must be simultaneously satisfied:
1) eigenvalues and eigenvectors, or calculated scattering parameters and hybrid optimization initial matrix MeAn approximation of;
2) the non-zero element positions correspond to the actual filter structure;
3) the coupling condition and the size rule reflected by the matrix elements need to be consistent with the size relation of the actual filter.
The features and properties of the present invention are described in further detail below with reference to examples.
Example 1
In this embodiment, a finite element electromagnetic simulation is used to perform a five-order microstrip direct coupling filtering as shown in fig. 2, and then the decoupling transformation is performed by using the hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of the present invention, which specifically includes the following steps:
step S1, obtaining a hybrid optimization initial matrix M through a synthesis method and rotation eliminatione；
(1) Obtaining a coupling matrix M by adopting a filter coupling matrix synthesis method;
(2) performing rotation elimination on the coupling matrix M by multiplying the rotation matrix by multiple iterations, and taking the matrix after the rotation elimination as a hybrid optimization initial matrix Me. The elimination sequence of the rotary elimination element of the embodiment is from right to left, first, back and row alternate, and the rotation points are (5, 6) (4, 5) (3, 4)(2, 3) (3, 4) (4, 5) (5, 6) (4, 5) (3, 4) (4, 5), and a hybrid optimization initial matrix M obtained by rotation eliminationeComprises the following steps:
step S2, optimizing the initial matrix M based on mixingePerforming decoupling transformation in the global optimization stage according to the optimization constraint conditions and the optimization fitness index to obtain a global optimization matrix Md(ii) a In this embodiment, a genetic algorithm is used as the global optimization algorithm.
(1) Hybrid optimization of an initial matrix M according to genetic algorithm characteristicseCarrying out global optimization to obtain an initialization matrix M'dInitialization matrix M'dThe matrix form of (a) is shown in fig. 3, and encoding processing is performed on matrix elements in global optimization, and encoding is performed according to a selected genetic algorithm to form a continuous parameter optimization genome (optimization parameters); wherein, the optimization constraint condition comprises: global optimization is performed according to the coupling condition and the topological structure of the filter, as shown in table 1, the initialization is performed randomly within a certain positive and negative range of an initial value, and the size relationship or the symmetrical relationship of elements having the size relationship or the symmetrical relationship is maintained in the whole optimization process.
Table 1, the design feature size of the filter and the coupling matrix element comparison table:
(2) defining a global optimization fitness index e _ obj:
e_obj＝(Siid-Siie)2；
wherein S isiidRepresenting a decoupled transform matrix MdReflection coefficient S of11Or S22；SiieRepresenting a hybrid-optimized initial matrix MeReflection coefficient S of11Or S22。
Further, the conversion calculation formula of the coupling matrix M-scattering parameter matrix S is:
Sii＝1+2jR1[Z-1]ii；
where Z ═ ω U-jR + M, ω is the normalized frequency, U is the unit matrix of the same order as the coupling matrix M, R is the zero matrix of the same order as the coupling matrix M, except for 1 row and 1 column of elements R in R, N rows and 1 column11＝R1，RN1＝RN，RNIs the normalized source load impedance.
(3) Utilizing the global optimization fitness index e _ obj and adopting a genetic algorithm to initialize a matrix M'dCarrying out iterative adjustment until the optimization result meets the precision requirement, and obtaining a global optimization matrix Md：
Step S3, the global optimization matrix M is processed by gradient algorithmdThe matrix elements are locally optimized, and a final decoupling transformation matrix M is output0：
Step 3.1, calculating the derivative of the matrix element in the local optimization:
(1) adopting the global optimization fitness index e _ obj in the step 2 as a gradient optimization objective function;
(2) with S11For optimizing the target, respectively deriving each element in the coupling matrix M by using a gradient optimization objective function and a conversion calculation formula of the coupling matrix M-scattering parameter matrix S to obtain a derivative J of each elementkl. For the matrix elements with the main and secondary symmetry relationship, the derivative of any one element is shared. As shown in fig. 3, m32, m56 and m65, in which the matrix elements m23 are symmetrically located, all adopt the derivative of m23 in the local optimization iteration process.
Step 3.2, defining iteration step length h of matrix elements in gradient algorithmkl：
It should be noted that, since each element in the coupling matrix M is a real number, an iteration step h needs to be takenklThe real part of the calculation of (2) is taken as the iteration step. The matrix elements participating in the local optimization in this case are m12, m23, m34, m22, m33, m44, m24, m25, m35, m26 and the elements at the aforementioned positions symmetrical about the primary and secondary. For the matrix elements with the main and secondary symmetry relationship, the common iteration step size is shown in FIG. 3, wherein m32, m56 and m65 of the symmetric positions of m23 of the matrix elements share the common iteration step size h in the local optimization iteration process23。
Step 3.3, using e _ obj as a local optimization convergence index according to the iteration step length hklPerforming iteration adjustment of local optimization, finishing iteration when the requirement of solving precision is met, and outputting a final decoupling transformation matrix M0：
Final decoupling transformation matrix M0The matrix element size relationship and the symmetry relationship in (1) satisfy the correspondence given in table 1. Separately hybrid optimized initial matrix MeGlobal optimization matrix MaAnd a final decoupling transformation matrix M0S parameters of (3), as shown in fig. 4 and 5, to finally decouple the transformation matrix M0The S parameter curve more approaches to the hybrid optimization initial matrix MeAnd the requirement of engineering precision is met. At the same time, it can be seen from table 2 that the transformation matrix M is finally decoupled0The eigenvalues of (A) are also more approximate to the initial matrix M of the hybrid optimizatione。
Table 2, eigenvalue comparison table:
case verification shows that the decoupling transformation method of the filter coupling matrix based on the hybrid optimization algorithm has good applicability to the decoupling transformation of the filter coupling matrix, so that the coupling matrix optimally solved can accurately approach the actual characteristics of the filter.
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (10)
1. A decoupling transformation method of a filter coupling matrix based on a hybrid optimization algorithm is characterized by comprising the following steps:
step S1, obtaining a hybrid optimization initial matrix M through a synthesis method and rotation eliminatione；
Step S2, optimizing the initial matrix M based on mixingePerforming decoupling transformation in the global optimization stage according to the optimization constraint conditions and the optimization fitness index to obtain a global optimization matrix Md；
Step S3, the global optimization matrix M is processed by gradient algorithmdThe matrix elements are locally optimized, and a final decoupling transformation matrix M is output0。
2. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of claim 1, wherein the step S1 specifically comprises:
(1) obtaining a coupling matrix M by adopting a filter coupling matrix synthesis method;
(2) performing rotation elimination on the coupling matrix M by multiplying the rotation matrix by multiple iterations, and taking the matrix after the rotation elimination as a hybrid optimization initial matrix Me。
3. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of claim 1, wherein the step S2 specifically comprises:
(1) hybrid optimization initial matrix M according to global optimization algorithm characteristicseCarrying out global optimization to obtain an initialization matrix M'dEncoding the matrix elements in the global optimization, and encoding the matrix elements into optimization parameters according to the selected global optimization algorithm; wherein, the optimization constraint conditions include that the global optimization needs to be initialized randomly according to a certain positive and negative range of an initial value according to the coupling condition and the topological structure of the filter, and the whole optimization process is carried out on elements with a size relationship or a symmetric relationshipThe magnitude relationship or symmetry relationship is maintained.
(2) Defining a global optimization fitness index e _ obj:
e_obj＝(Siid-Siie)2；
wherein S isiidRepresenting a decoupled transform matrix MdReflection coefficient S of11Or S22；SiieRepresenting a hybrid-optimized initial matrix MeReflection coefficient S of11Or S22；
(3) Utilizing the global optimization fitness index e _ obj to adopt a global optimization algorithm to initialize a matrix M'dCarrying out iterative adjustment until the optimization result meets the precision requirement, and obtaining a global optimization matrix Md。
4. The hybrid optimization algorithm-based decoupling transformation method for the coupling matrix of the filter according to claim 1, wherein the conversion calculation formula of the coupling matrix M-scattering parameter matrix S is as follows:
Sii＝1+2jR1[Z-1]ii；
where Z ═ ω U-jR + M, ω is the normalized frequency, U is the unit matrix of the same order as the coupling matrix M, R is the zero matrix of the same order as the coupling matrix M, except for 1 row and 1 column of elements R in R, N rows and 1 column11＝R1，RN1＝RN，RNIs the normalized source load impedance.
5. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method according to claim 1, wherein step 3 specifically comprises:
step 3.1, calculate the derivative J of the matrix elements in the local optimizationkl；
Step 3.2, according to the derivative J of the matrix elementklCalculating an iteration step hkl：
Step 3.3, take e _ obj as officePartially optimizing the convergence index according to the iteration step length hklPerforming iteration adjustment of local optimization, finishing iteration when the requirement of solving precision is met, and outputting a final decoupling transformation matrix M0。
6. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method according to claim 5, wherein the step 3.1 is specifically:
(1) adopting the global optimization fitness index e _ obj in the step 2 as a gradient optimization objective function;
(2) with S11For optimizing the target, respectively deriving each element in the coupling matrix M by using a gradient optimization objective function and a conversion calculation formula of the coupling matrix M-scattering parameter matrix S to obtain a derivative J of each elementkl。
7. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of claim 5, wherein derivatives of any one of the elements are shared for matrix elements having primary and secondary symmetry relationships.
8. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of claim 5, wherein iteration steps are shared for matrix elements having a primary and secondary symmetry relationship.
9. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of claim 5, wherein in step 3.2, iteration step h is takenklThe real part of the calculation of (2) is taken as the iteration step.
10. The hybrid optimization algorithm-based filter coupling matrix decoupling transformation method of claim 5, wherein a final decoupling transformation matrix M0The following decoupling transformation conditions must be simultaneously satisfied:
1) eigenvalues and eigenvectors, or calculated scattering parameters and hybrid optimization initial matrix MeAn approximation of;
2) the non-zero element positions correspond to the actual filter structure;
3) the coupling condition and the size rule reflected by the matrix elements need to be consistent with the size relation of the actual filter.
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