Two-level optimization algorithm for microwave filter coupling matrix transformation

Abstract

The present invention relates to the field of microwave filters, and discloses a two-layer optimization algorithm applied to the coupling matrix transformation of microwave filters, which abstracts the coupling matrix topological transformation problem into an optimization problem and adopts the idea of ​​hierarchical optimization to solve it; in the first layer optimization, an adaptive differential evolution algorithm is used to solve the optimization problem, and a solution with better performance is searched in a larger optimization space. The adaptive differential evolution algorithm is an optimization algorithm based on swarm intelligence, which can approach the optimal solution through continuous iteration of the swarm. By using this algorithm, a relatively good solution can be found. In the second layer optimization, based on the solution obtained by the first layer optimization, an adaptive quasi-Newton method is used to solve the optimization problem, and a solution with better performance is quickly searched in the local optimization space. The quasi-Newton method is iterated based on gradient information, and only needs to calculate the approximate value of the inverse matrix of the Hessian matrix, so the calculation efficiency is high.

Description

Technical Field

[0001] The invention relates to the field of microwave filters, and in particular to a two-layer optimization algorithm applied to coupling matrix transformation of microwave filters. Background Art

[0002] In the design and debugging of microwave filters, the coupling matrix is ​​a commonly used mathematical model. The comprehensive method based on the coupling matrix has been used for the design of filters under the cross-coupling structure. However, it is usually difficult to accurately correspond between the coupling matrix topology and the filter structure, and some coupling matrix topologies are not physically feasible and have no practical value. Therefore, the initial coupling matrix must be converted into a coupling matrix of a specified topology with the same scattering parameters. In addition to microwave filter design, finding the coupling matrix transformation of arbitrary topology is also related to filter debugging. After the microwave filter is processed, the designer usually extracts the unloaded quality factor and resonator coupling value based on the scattering data, and then debugs the filter to obtain a filter that meets the design requirements.

[0003] In recent years, various coupling matrix topology transformation methods have been proposed. These methods usually rely on the similarity transformation of the coupling matrix and do not affect the eigenvalues ​​of the coupling matrix. Therefore, although these transformations modify the coupling values, they do not affect the scattering parameters of the input / output ports. In 2007, RJ Cameron et al. published an article titled "An Exhaustive Approach to the Coupling Matrix Synthesis Problem Application to the Design of High Degree Asymmetric Filters" in the International Journal of RF and Microwave Computer-Aided Engineering, Vol. 17, No. 1, which proposed a method of using an exhaustive method to obtain the coupling matrix under a specified topology. Although this method can find all solutions to the problem, because it involves symbolic calculations of the Groebner basis, the algorithm is very complex in computation and difficult to be directly applied to practical problems.

[0004] In addition to analytical methods, the use of optimization algorithms to solve the topological transformation of coupling matrices has also been widely studied. In 2000, S. Amari et al. published a paper titled "Synthesis of Cross-Coupled Resonator Filters Using an Analytical Gradient-Based Optimization Technique" in IEEE Transactions on Microwave Theory and Techniques, No. 48, No. 9, which proposed a method of using an exhaustive method to obtain the coupling matrix under a specified topology. The local optimization method is used to find a solution that satisfies both the same scattering parameter coefficients and the matrix topology conditions. However, since the local optimization algorithm is prone to fall into local extreme values, it is difficult to obtain a satisfactory solution, resulting in the mismatch between the optimized scattering parameters and the expected scattering parameters. In 2007, M.Uhm et al. published the article "Synthesis of ResonatorFilters with Arbitrary Topology Using Hybrid Method" in IEEE Transactions on Microwave Theory and Techniques, issue 55, issue 10. In order to avoid convergence to local extrema, a genetic algorithm was used to solve the coupling matrix transformation problem that meets the scattering parameters and structural requirements, but the time cost of converging to the optimal solution is relatively long. In order to speed up the convergence of the optimization algorithm, in 2019, X.Luo et al. published the article "AdaptiveSynthesis for Resonator-Coupled Filters Based on Particle Swarm Optimization" in IEEE Transactions on Microwave Theory and Techniques, issue 67, issue 2. The particle swarm algorithm was used to solve the coupling matrix transformation problem, but the algorithm is prone to fall into local extrema, resulting in a low success rate of coupling matrix topology conversion, and the optimization time cost improvement effect is not obvious. For this reason, we propose a two-layer optimization algorithm for microwave filter coupling matrix transformation. Summary of the invention

[0005] 1. Technical issues to be solved

[0006] In view of the deficiencies of the prior art, the present invention provides a two-layer optimization algorithm applied to microwave filter coupling matrix transformation to solve the above-mentioned problems.

[0007] (II) Technical solution

[0008] To achieve the above-mentioned purpose, the present invention provides the following technical solution: a two-layer optimization algorithm applied to microwave filter coupling matrix transformation, comprising the following steps:

[0009] Step 1: Establish the objective function of topological transformation of microwave filter coupling matrix;

[0010] Step 2: Use the adaptive differential evolution algorithm to obtain the optimal solution for the topological transformation of the first-layer coupling matrix of the microwave filter;

[0011] Step 3: Near the initial solution of the coupling matrix, use the adaptive quasi-Newton algorithm to obtain the filter coupling matrix after conversion.

[0012] Preferably, the specific content of the first step is:

[0013] S1: According to the expected response of the microwave filter, the coupling matrix [ABCD] matrix is ​​obtained, and then the full coupling matrix M of the microwave filter is obtained. q , further simplify the full coupling matrix of the microwave filter and obtain the folded coupling matrix M before conversion b ;

[0014] S2: Obtain the topological matrix T after the coupling matrix transformation;

[0015] S3: Obtain the similarity matrix Q, which is composed of the design variables x;

[0016] S4: According to the folded coupling matrix M b And the similarity matrix Q to obtain the matrix M after topological transformation a ;

[0017] S5: According to the transformed matrix M a , topological matrix T and similarity matrix Q are used to establish the objective function of topological transformation.

[0018] Preferably, the specific content of the second step is:

[0019] S1: Determine the stopping condition of the first-level optimization algorithm;

[0020] S2: Determine the optimization space of the first-level optimization algorithm;

[0021] S3: In order to increase the convergence speed of the optimization algorithm, a population size adaptive differential evolution algorithm is proposed.

[0022] Preferably, the specific content of the third step is:

[0023] S1: Determine the stopping condition of the second-level optimization algorithm;

[0024] S2: Taking the optimal solution obtained by the first-level optimization algorithm as the initial value, the adaptive quasi-Newton method is used to obtain a better solution;

[0025] S3: In order to prevent the quasi-Newton method from converging to the local extreme solution, an initial solution adaptive quasi-Newton method is proposed. The quasi-Newton method is used to obtain a better solution as the initial solution, and the quasi-Newton method is used again for optimization until the quasi-Newton method reaches the stopping condition.

[0026] (III) Beneficial effects

[0027] Compared with the prior art, the present invention provides a two-layer optimization algorithm for microwave filter coupling matrix transformation, which has the following beneficial effects:

[0028] 1. Compared with the traditional method, the two-layer optimization algorithm for microwave filter coupling matrix transformation of the present invention combines the search advantage of adaptive differential evolution in a large space and the convergence advantage of adaptive quasi-Newton method in a small space, thereby improving the efficiency of microwave filter coupling matrix transformation.

[0029] 2. The two-layer optimization algorithm applied to the microwave filter coupling matrix transformation can obtain a microwave filter coupling matrix topology transformation result with better performance, which plays an important role in the application of microwave filters in wireless communications, radar systems and satellite communications. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 is a flow chart of the research algorithm of the present invention;

[0031] Figure 2 A schematic diagram of population size change in the adaptive differential evolution used in the present invention;

[0032] Figure 3 A schematic diagram of the adaptive quasi-Newton algorithm used in the present invention;

[0033] Figure 4 Schematic diagram of the evolution curve for solving the topological transformation of the coupling matrix of an eighth-order microwave filter using a hierarchical optimization algorithm;

[0034] Figure 5 The evolutionary algebraic diagram of the topological transformation of the coupling matrix of the eighth-order microwave filter;

[0035] Figure 6 Solve the S-curve diagram of the coupling matrix of the eighth-order microwave filter before and after the topological transformation for the hierarchical optimization algorithm;

[0036] Figure 7 Schematic diagram of the evolution curve of the topological transformation of the coupling matrix of the tenth-order microwave filter solved by the hierarchical optimization algorithm;

[0037] Figure 8 The evolutionary algebraic diagram of the topological transformation of the coupling matrix of the tenth-order microwave filter;

[0038] Fig. 9 The S-curve diagram before and after the topology transformation of the coupling matrix of the tenth-order microwave filter is solved by the hierarchical optimization algorithm. DETAILED DESCRIPTION

[0039] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0040] See also Figure 1-9 , a two-level optimization algorithm applied to microwave filter coupling matrix transformation, including the following steps:

[0041] According to the design indicators including the order N=8, return loss (20dB) and transmission zero point (1.25, -1.5, 1.7) of the microwave filter, the transmission polynomial and characteristic polynomial are determined, and the [ABCD] matrix of the microwave filter is obtained according to the characteristic polynomial, and the omnidirectional coupling matrix M of the microwave filter is obtained by evolution. q , as shown in formula (1). The folded matrix M before topological transformation is extracted from the polynomial b , as shown in formula (2); give the expanded box topology matrix T, as shown in formula (3); determine the similarity matrix Q of the coupling matrix transformation, as shown in formula (4); according to the matrix M b and Q to obtain the matrix M after topological transformation a , as shown in formula (6). According to the transformed matrix M a , expand the box-type topology matrix T and the similarity matrix Q to establish the objective function of topology transformation, as shown in formula (7).

[0042]

[0043]

[0044]

[0045]

[0046] Where x=[x1,x2,…,x 28 ] is the optimization variable.

[0047] The coupling matrix after topological transformation:

[0048] M a =M b T QM b (5)

[0049]

[0050] In the formula, ⊙ represents the multiplication of the corresponding elements of two matrices, D e is the diagonal identity matrix.

[0051] (2) Use the population size adaptive differential evolution algorithm to obtain the optimal solution for the first-level optimization. The stopping condition of the first-level optimization algorithm is that the optimization objective function value f(x) < 1e -2 Or the number of optimization iterations is less than 20,000; in order to improve the search ability of the algorithm, the population size decreases as the number of evolutionary generations increases, and changes linearly, as shown in the following formula:

[0052]

[0053] Where N init is the initial population size, N min is the minimum population size, N max is the maximum population size, N G and N G+1 is the population size of the Gth and G+1th generations, and round(·) is the rounding function.

[0054] (3) Taking the optimal solution of the first-level optimization as the initial solution, the adaptive quasi-Newton algorithm is used to obtain the optimal solution of the second-level optimization. The stopping condition of the second-level optimization algorithm is that the optimization objective function value f(x) < 1e -7 Or the number of optimization iterations is less than 1000.

[0055] (4) The hierarchical optimization algorithm of the present invention was run 50 times, and the success rate reached 92%. The restart strategy was used to further improve the success rate of the algorithm. After restarting once, the probability of algorithm failure was (1-92%). 2 =0.64%, so the probability of a successful restart of the algorithm is 1-0.64%=99.36%.

[0056] Table 1: Coupling matrix of the eighth-order microwave filter after topological transformation using the hierarchical optimization algorithm of the present invention

[0057] S 1 2 3 4 5 6 7 8 L S 0 0.987 0 0 0 0 0 0 0 0 1 0.987 0.006 0.092 0 0.811 0 0 0 0 0 2 0 0.092 -0.927 -0.270 0 0 0 0 0 0 3 0 0 -0.270 0.16 -0.358 -1.029 -0.477 0 0 0 4 0 0.811 0 -0.358 0.019 0.431 0 0 0 0 5 0 0 0 0 0.431 0.017 -0.494 0.634 0 0 6 0 0 0 -0.477 0 -0.494 -0.006 0 -0.798 0 7 0 0 0 0 0 0.634 0 0.281 -0.171 0 8 0 0 0 0 0 0 -0.798 -0.171 0.006 0.987 L 0 0 0 0 0 0 0 0 0.987 0

[0058] Table 2: Results of topological transformation of coupling matrix of eighth-order microwave filter solved by the hierarchical optimization algorithm of the present invention fifty times

[0059]

[0060] Table 3: Coupling matrix of the tenth-order microwave filter after topological transformation using the hierarchical optimization algorithm of the present invention

[0061]

[0062]

[0063] Table 4: The topological transformation results of the coupling matrix of the tenth-order microwave filter solved by the hierarchical optimization algorithm of the present invention fifty times

[0064]

[0065] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A two-layer optimization algorithm for microwave filter coupling matrix transformation, characterized in that: The following steps are involved: Step 1: Establish the objective function of topological transformation of microwave filter coupling matrix; The specific steps are: S1: According to the expected response of the microwave filter, the coupling matrix [ABCD] matrix is ​​obtained, and then the full coupling matrix M of the microwave filter is obtained. q , further simplify the full coupling matrix of the microwave filter and obtain the folded coupling matrix M before conversion b ; S2: Obtain the topological matrix T after the coupling matrix transformation; S3: Obtain the similarity matrix Q, which is composed of the design variables x; S4: According to the folded coupling matrix M b And the similarity matrix Q to obtain the matrix M after topological transformation a ; S5: According to the transformed matrix M a , topological matrix T and similarity matrix Q are used to establish the objective function of topological transformation; Step 2: Use the adaptive differential evolution algorithm to obtain the optimal solution for the topological transformation of the first-layer coupling matrix of the microwave filter; Step 3: Near the initial solution of the coupling matrix, use the adaptive quasi-Newton algorithm to obtain the filter coupling matrix after conversion.

2. The two-layer optimization algorithm for microwave filter coupling matrix transformation according to claim 1 is characterized in that: The specific contents of the second step are: S1: Determine the stopping condition of the first-level optimization algorithm; S2: Determine the optimization space of the first-level optimization algorithm; S3: In order to increase the convergence speed of the optimization algorithm, a population size adaptive differential evolution algorithm is proposed.

3. The two-layer optimization algorithm for microwave filter coupling matrix transformation according to claim 1 is characterized in that: The specific content of the third step is: S1: Determine the stopping condition of the second-level optimization algorithm; S2: Taking the optimal solution obtained by the first-level optimization algorithm as the initial value, the adaptive quasi-Newton method is used to obtain a better solution; S3: In order to prevent the quasi-Newton method from converging to the local extreme solution, an initial solution adaptive quasi-Newton method is proposed; the quasi-Newton method is used to obtain a better solution as the initial solution, and the quasi-Newton method is used again for optimization until the quasi-Newton method reaches the stopping condition.

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