Design method of asymmetric three-passband filter based on frequency-variable coupling structure

Abstract

The invention belongs to the technical field of electromagnetic fields and microwaves, and particularly relates to a design method of an asymmetric three-passband filter based on a frequency-variable coupling structure. According to the method, a frequency-dependent coupling structure is applied to the design of the asymmetric three-passband filter based on the REMEZ-like algorithm, and after a frequency-dependent coupling matrix corresponding to a topological structure is converted into a non-frequency-dependent coupling matrix, all unknown parameters of the frequency-dependent coupling matrix are optimized and solved through a constrained nonlinear minimization function; therefore, an original cross coupling path is eliminated; and the generated N-1 transmission zeros can be generated and independently controlled by the frequency-variable coupling structure, so that the topological structure of the filter is simplified, and the debugging complexity is reduced. The three-passband filter with different orders, return losses and bandwidths can be synthesized in different passbands and specified transmission zero points, an in-line topological structure is achieved, the difficulty of filter design and simulation is lowered, and the degree of out-of-band rejection and isolation between the passbands is greatly improved.

Description

Technical Field

[0001] This invention belongs to the field of electromagnetic field and microwave technology, and particularly relates to the design of three-passband filters, specifically a design method for an asymmetric three-passband filter based on a frequency-variable coupling structure. Background Technology

[0002] In modern microwave filter design, the introduction of transmission zeros plays a decisive role in improving out-of-band rejection performance. Cross-coupling technology, with its topological flexibility in implementing transmission zeros, has been widely applied in microwave filter structures. Compared to traditional filter architectures, cross-coupled filters exhibit significant advantages in achieving miniaturized structures, high-efficiency operation, excellent out-of-band rejection characteristics, high rectangular coefficients, and flexible design. Currently, most cross-coupled structures are cascaded triplet (CT) and cascaded quadruplet (CQ) structures. The former allows independent control of one transmission zero position, while the latter, although capable of implementing two transmission zeros, requires the two zeros to be symmetrical, reducing design freedom. Furthermore, the coexistence of multiple coupling paths, while generating transmission zeros, also leads to a significant increase in debugging difficulty and topological complexity. To address this technological bottleneck, frequency-varying coupling mechanisms have become a research hotspot in recent years. Frequency-variable coupling structures can achieve a transmission zero point through a single coupling path. Filters built based on the principle of frequency-variable coupling can not only optimize the topology to achieve in-line topology, but also independently control the position of the transmission zero point to achieve asymmetry, thus improving design freedom and effectively reducing debugging complexity. However, synthesizing the frequency-variable coupling matrix using traditional direct matrix methods is computationally complex and has strict requirements on the topology.

[0003] With the trend of integrated development in wireless communication systems, the demand for multi-band filters, especially three-passband filters, is becoming increasingly urgent. Currently, three-passband filters are mainly implemented using three methods: the first is the multi-mode resonator method, the second is the frequency transformation method, and the third is the iterative synthesis method. The iterative synthesis method obtains the three-passband filter function by introducing optimization techniques and iterative methods, making it more flexible and simpler.

[0004] Some scholars have proposed using a REMEZ-like algorithm to design asymmetric three-passband filters. Such filters can achieve different passbands with different bandwidths, orders, and return losses. However, this technical solution has problems such as difficulty in electromagnetic simulation convergence and complexity in the design process due to too many cross-coupling paths, which urgently need to be solved. Summary of the Invention

[0005] To address the aforementioned problems and shortcomings, and to resolve the difficulty in simulation and design caused by excessive cross-coupling paths in existing asymmetric three-passband filters, this invention provides a design method for an asymmetric three-passband filter based on a frequency-variable coupling structure. The designed asymmetric three-passband filter achieves different bandwidths, orders, and return losses for different passbands; it also eliminates all cross-couplings in the filter, realizing an in-line topology and simplifying the design and simulation of the filter.

[0006] A design method for an asymmetric three-passband filter based on a frequency-variable coupling structure, the specific steps of which are as follows:

[0007] Step 1: For an asymmetric three-pass band filter, the filter's transfer function is related to the filtering function:

[0008]

[0009] In the formula, ε is the ripple factor; C(ω) is the filter function, which is the ratio of two polynomials F(ω) to P(ω):

[0010]

[0011] The order of F(ω) is N, and the root zF of F(ω) is the reflection zero RZs of the filter; the order of P(ω) is nz, and its root is the transmission zero TZs of the filter, which is given according to the design specifications.

[0012] The orders of the three passbands are set, that is, the distribution of the roots zF of the polynomial F in each passband is as follows: n1 in passband one, n2 in passband two, and n3 in passband three (n1+n2+n3=N). The ranges of the three passbands are (a, b), (c, d), and (e, f), where a, b, c, d, e, and f are constants determined by the design requirements.

[0013] The synthesis of the filter function involves finding N coefficients of F(ω), which can be uniquely determined by interpolating a set of (N+3) points; the (N+3) critical frequency points for C(ω) interpolation are shown below:

[0014]

[0015] Where ω 1,1 =a、 ω 2,1 =c、 ω 3,1 =e、 These are the band edges of the three passbands. Initially, the frequency point interpolation is spaced equally in each passband.

[0016] Within each passband, the interpolation-corresponding C(ω) value is ±Δ. k(k = 1, 2, 3, corresponding to three passbands), the negative sign is taken alternately in each passband. S(ω) represents the sign of each value of C(ω) in the passband.

[0017]

[0018] The N coefficients of F(ω) are calculated using a REMEZ-like algorithm, i.e., by solving (N+3) linear equations, and are expressed in matrix form as follows:

[0019]

[0020] M = [M1M2]

[0021]

[0022] Where f′2, f′3…f′ N+1 These are the coefficients of polynomial F, and f′1=1 is the highest-order coefficient, f′ N+1 It is a zero-order coefficient. It's important to note that the peak value is generally different for each frequency band. To apply the minimum return loss RL, we must first determine the band with the largest return loss, and then apply the required RL to that band. Therefore, ε is defined as follows:

[0023]

[0024] ω m It is one of the interpolations within the maximum peak passband; until the N initial coefficients of F(ω) are solved.

[0025] Step 2: Update the N coefficients of F(ω) and their corresponding interpolation points using the iterative process of the Remez algorithm from Step 1. and These are the band edges of the three passbands, which do not change with iteration.

[0026] The algorithm iterates until the filter function obtains an equal ripple response, thus obtaining the N coefficients of the polynomial F(ω).

[0027] Step 3: Based on the polynomial F(ω) obtained after iteration in Step 2, and combined with filter synthesis theory, obtain the S-parameters and transverse coupling matrix M of the asymmetric three-passband filter. tran .

[0028] Step 4: Select the topology suitable for the asymmetric three-pass band filter, and transform the frequency-varying coupling matrix containing unknown parameters corresponding to the topology into a non-frequency-varying coupling matrix M through matrix similarity transformation. final Set the optimization objective function; then, based on the horizontal coupling matrix M... tranSolving the non-frequency-varying coupling matrix M using the fmincon function final The invention obtains all the parameters of the frequency-varying coupling matrix of the asymmetric three-pass band filter, and then synthesizes all the unknown parameters of the frequency-varying coupling matrix, thus completing the entire design. This invention avoids the complex calculations required for synthesizing the frequency-varying coupling matrix using the traditional direct matrix method and is applicable to the vast majority of topologies.

[0029] This invention relates to an asymmetric three-passband filter based on a frequency-variable coupling structure, which has the following advantages:

[0030] 1. By using the optimization method proposed in step 4, all unknown parameters of the frequency-varying coupling matrix corresponding to the topology are solved. The frequency-varying coupling structure is then applied to the design of an asymmetric three-passband filter similar to the Remez algorithm, eliminating the original cross-coupling path. The designed transmission zeros can be generated and independently controlled by the frequency-varying coupling structure, further simplifying the filter topology and reducing the complexity of debugging.

[0031] 2. Compared with the traditional design of three-passband filters based on the Remez-like algorithm, the three-passband filter algorithm designed in this invention can quickly iterate and converge to obtain the equal ripple response in step 1, which significantly reduces the calculation time. Furthermore, it can design three-passband filters with different orders, return losses, and bandwidths in different passbands and specified transmission zeros. Attached Figure Description

[0032] Figure 1 This is a graph showing the iterative changes of the filter function C(ω) and interpolation points of the asymmetric frequency-variable three-band filter in the embodiment.

[0033] Figure 2 This is a schematic diagram of the S-parameters obtained from the theoretical polynomial of the asymmetric frequency-variable three-band filter in the embodiment.

[0034] Figure 3 The transverse matrix M of the asymmetric frequency-variable three-band filter in this embodiment is... trans ;

[0035] Figure 4 This is the frequency-variable coupling topology of the embodiment;

[0036] Figure 5 This is a schematic diagram of the S-parameters of the frequency-varying coupling matrix obtained through optimization in the embodiment.

[0037] Figure 6 This is the frequency-varying coupling matrix of the asymmetric frequency-varying three-pass band filter in the embodiment;

[0038] Figure 7 This is a flowchart of the present invention. Detailed Implementation

[0039] The following describes the embodiments and appendices. Figure 1-6The content of this invention will be further explained.

[0040] A design method for an asymmetric three-passband filter based on a frequency-variable coupling structure, the specific steps of which are as follows:

[0041] Step 1: For the target asymmetric three-passband filter, set the distribution of the roots zF of its filter function polynomial F(ω) in each passband: n1=3, n2=3, n3=3, filter order N=n1+n2+n3=9, normalized bandwidths of the three passbands are set to (-1, -0.7), (-0.2, 0.2) and (0.7, 1), and normalized transmission zero Ω. TZ = [-0.59, -0.49, 0.56, 0.42, -2, 1.8], and the polynomial P(ω) can be obtained based on the set normalized transmission zeros.

[0042] In this embodiment, 12 points need to be interpolated to iteratively generate the coefficients of the polynomial F(ω). Since the 12 points are uniformly distributed within the passband, the initial interpolation points are set as follows:

[0043] ω 1,1 =-1、ω 1,2 =-0.9、ω 1,3 =-0.8、ω 1,4 =-0.7、ω 2,1 =-0.2、ω 2,2 =-0.1、ω 2,3 =0.1, ω 2,4 =0.2, ω 3,1 =0.7, ω 3,2 =0.8, ω 3,3 =0.9, ω 3,4 =1.

[0044] Step 2: Substitute the 12 interpolation points into the REMEZ-like algorithm from Step 1, and iterate until the filter function exhibits an equal ripple response. This will yield the final coefficients of the polynomial F(ω), completing the solution for the N initial coefficients of F(ω).

[0045] Step 3: Based on the polynomial F(ω) obtained after iteration in Step 2, the filter function C(ω) generated by the iteration and the changes in the interpolation points are as follows: Figure 1 , Figure 1 The solid blue line represents the filter function before the iteration begins; the initial interpolated data is marked with "+". After iteration, the new interpolated data is marked with "x". The dashed red line represents the filter function obtained after the iteration ends. After obtaining the polynomial F(ω), the S-parameters and transverse coupling matrix M of the three-passband filter can be calculated according to the synthesis theory of the filter. trans .

[0046] Step 4: In this embodiment, the asymmetric three-passband filter to be designed has a passband width of 100MHz, a center frequency of 2000MHz, and six transmission zeros at 1971MHz, 1976MHz, 2028MHz, 2021MHz, 1903MHz, and 2092MHz respectively. The first passband bandwidth is 1950MHz-1965.3MHz; the second passband bandwidth is 1990MHz-2010MHz; and the third passband bandwidth is 2035.3MHz-2050MHz. Its S-parameter diagram is shown below. Figure 2 As shown, the lateral coupling matrix is ​​as follows Figure 3 As shown.

[0047] Finally, based on the obtained transverse coupling matrix of the three-passband filter, the frequency-varying coupling matrix is ​​synthesized, and the selected topology is as follows. Figure 4 The diagram shows an inline (line-type topology), where the six transmission zeros are controlled and formed by frequency-varying coupling between cavity 2 and cavity 3, between cavity 3 and cavity 4, between cavity 4 and cavity 5, between cavity 5 and cavity 6, between cavity 6 and cavity 7, and between cavity 7 and cavity 8, respectively. The frequency-varying coupling matrix is ​​then transformed into a non-frequency-varying coupling matrix M through matrix similarity transformation. final .

[0048] The objective function of the optimization method is Cost = (λ) trans -λ final ) T (λ trans -λ final ), where λ final The corresponding non-frequency-varying coupling matrix M after matrix transformation final The relevant eigenvalues, λ trans Corresponding horizontal coupling matrix M trans The relevant eigenvalues, where T is the transpose sign. in λ represents the eigenvalues ​​of the lateral coupling matrix. i c λ represents the eigenvalues ​​of the matrix formed by removing the first row, first column, last row, and last column of the horizontal coupling matrix. i Z1 λ represents the eigenvalues ​​of the matrix formed by the elements remaining after removing the first row and first column of the horizontal coupling matrix. i Z2 λ represents the eigenvalues ​​of the matrix formed by removing the last row and last column of the horizontal coupling matrix. final The elements have the same properties as λ. trans The meaning is the same as the corresponding element.

[0049] Furthermore, the error of the objective function Cost is less than 1*10. -7 To ensure that the S-parameter response of the optimized frequency-varying coupling matrix is ​​consistent with that of the original transverse coupling matrix M tran The response remains consistent.

[0050] For the objective function described above, optimization using the constrained nonlinear minimization function fmincon yields the frequency-varying coupling matrix of the specified topology. In this embodiment, the error of the objective function Cost is less than 1*10^6. -10 In obtaining such Figure 6 After obtaining the asymmetric three-band frequency-varying coupling matrix shown, the classical coupling matrix synthesis method can be applied to obtain the following... Figure 5 The S-parameters are shown.

[0051] As can be seen from the above embodiments, when synthesizing asymmetric frequency-varying three-passband filters based on a REMEZ-like iterative algorithm, the present invention has fast iterative convergence, requiring only 3 iterations to achieve an equal ripple response, greatly reducing computation time; the results of the optimized algorithm agree well with the theoretical polynomial response, avoiding the complex calculations of synthesizing frequency-varying coupling matrices using traditional direct matrix methods, and is applicable to most topologies, making the method more flexible and simpler.

[0052] This invention applies a frequency-varying coupling structure to the design of an asymmetric three-passband filter based on a Remez-like iterative algorithm. After converting the frequency-varying coupling matrix corresponding to the topology into a non-frequency-varying coupling matrix, all unknown parameters of the frequency-varying coupling matrix are solved by a constrained nonlinear minimization function, thus eliminating the original cross-coupling paths. The resulting N-1 transmission zeros can be generated and independently controlled by the frequency-varying coupling structure, simplifying the filter topology and reducing the complexity of debugging. N is the order of the filter. This invention can synthesize three-passband filters of different orders, return losses, and bandwidths in different passbands and with specified transmission zeros, realizing in-line topologies, simplifying filter design and simulation, and greatly improving out-of-band suppression and isolation between passbands. This invention provides a good optimization effect for engineering practice and has significant engineering value.

Claims

1. A design method for an asymmetric three-passband filter based on a frequency-variable coupling structure, characterized in that, The specific steps are as follows: Step 1: For the asymmetric three-passband filter, set the distribution of the roots zF of the polynomial F(ω) corresponding to its filter function in each passband: n1, n2, n3, filter order N, normalized bandwidths a, b, c, d, e, f of the three passbands, and normalized transmission zeros Ω. TZ The polynomial P(ω) is obtained based on the set normalized transmission zeros. The transfer function of a filter is related to the filtering function: In the formula, ε is the ripple factor; C(ω) is the filter function, which is the ratio of two polynomials F(ω) to P(ω): The order of F(ω) is N, and the root zF of F(ω) is the reflection zero RZs of the filter; the order of P(ω) is nz, and the root of P(ω) is the transmission zero TZs of the filter, which is given according to the design specifications. The order of the three passbands is set, that is, the distribution of the root zF of F(ω) in each passband is: n1 in passband one, n2 in passband two, and n3 in passband three (n1+n2+n3=N); the ranges of the three passbands are (a, b), (c, d), and (e, f), where a, b, c, d, e, and f are all constants determined by the design requirements; The synthesis of the filter function involves finding N coefficients of F(ω), which are uniquely determined by interpolating a set of (N+3) points. The (N+3) critical frequency points for interpolation of C(ω) are shown below: Where ω 1,1 =a、 ω 2,1 =c、 ω 3,1 =e、 These are the band edges of the three passbands; initially, the frequency point interpolation is spaced equally in each passband. Within each passband, the interpolation-corresponding C(ω) value is ±Δ. k The sign is alternated within each passband; where k = 1, 2, 3, corresponding to three passbands; S(ω) represents the sign of each value of C(ω) within the passband; The N coefficients of F(ω) are calculated using a REMEZ-like algorithm, i.e., by solving (N+3) linear equations, and are expressed in matrix form as follows: M = [M1M2] i∈(1,n1+1),j∈(1,n2+1),z∈(1,n3+1) Where f2′, f3′…f′ N+1 These are the coefficients of F(ω), and f′1=1 is the highest-order coefficient, f′ N+1 It is a zero-order coefficient; first, determine the largest band, then apply the required return loss RL to that band to apply the minimum return loss RL, therefore ε is defined as follows: ω m It is one of the interpolations within the maximum peak passband; until the N initial coefficients of F(ω) are solved; Step 2: Update the N coefficients of F(ω) and the corresponding interpolation points ω using the iterative process of the Remez algorithm from Step 1. 1,2 ω 1,3 … ω 2,2 ω 2,3 … ω 3,2 ω 3,3 … And ω 1,1 , ω 2,1 , ω 3,1 , These are the band edges of the three passbands, which do not change with iteration; until the algorithm iterates to the point where the filter function obtains an equal ripple response, so as to obtain the N coefficients of the polynomial F(ω); Step 3: Based on the polynomial F(ω) obtained after iteration in Step 2, and combined with filter synthesis theory, obtain the S-parameters and transverse coupling matrix M of the asymmetric three-passband filter. tran ; Step 4: Select the topology suitable for the asymmetric three-pass band filter, and transform the frequency-varying coupling matrix containing unknown parameters corresponding to the topology into a non-frequency-varying coupling matrix M through matrix similarity transformation. final Set the optimization objective function; At this point, based on the horizontal coupling matrix M tran Solving the non-frequency-varying coupling matrix M using the fmincon function final By obtaining all the parameters, we can synthesize all the unknown parameters of the frequency-varying coupling matrix of the asymmetric three-pass band filter, thus completing the entire design.

2. The design method for an asymmetric three-passband filter based on a frequency-variable coupling structure as described in claim 1, characterized in that, In step 4, based on the horizontal coupling matrix M tran Solving the non-frequency-varying coupling matrix M using the fmincon function final All parameters are as follows: Cost = (λ) trans -λ final ) T (λ trans -λ final Let ) be the objective function, where λ final The corresponding non-frequency-varying coupling matrix M after matrix transformation final The relevant eigenvalues, λ trans Corresponding horizontal coupling matrix M trans The relevant eigenvalues, where T is the transpose sign; in These are the eigenvalues ​​of the horizontal coupling matrix; The eigenvalues ​​are the matrix formed by removing the first row, first column, last row, and last column of the horizontal coupling matrix. The eigenvalues ​​are the matrix formed by the elements remaining after removing the first row and first column of the horizontal coupling matrix. λ represents the eigenvalues ​​of the matrix formed by the elements remaining after removing the last row and last column of the horizontal coupling matrix. final The elements have the same properties as λ. trans The meaning is the same as the corresponding element.

3. The design method of the asymmetric three-passband filter based on the frequency-variable coupling structure as described in claim 2, characterized in that: The error of the objective function Cost is less than 1*10. -7 .

4. The design method of the asymmetric three-passband filter based on the frequency-variable coupling structure as described in claim 1, characterized in that: The topology is in-line.

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