Design Method of an Asymmetric Dual-Band Filter Based on Frequency-Variable Coupling Structure

Abstract

The present invention belongs to the field of electromagnetic fields and microwave technologies, and specifically relates to a design method for an asymmetric dual-band filter based on a frequency-variable coupling structure. The present invention applies the frequency-variable coupling structure to the design of an asymmetric dual-band filter based on two low-pass prototype functions. After converting the frequency-variable coupling matrix corresponding to the topological structure into a non-frequency-variable coupling matrix, all unknown parameters of the frequency-variable coupling matrix are optimized and solved through a constrained non-linear minimization function, thereby eliminating the original cross-coupling paths. The N-1 transmission zeros generated can be generated and independently controlled by the frequency-variable coupling structure, simplifying the topological structure of the filter and reducing the complexity of debugging. The present invention can synthesize dual-band filters with different orders, return losses, and bandwidths in different passbands and specified transmission zeros, realize an in-line topological structure, simplify the difficulty of filter design and simulation, and greatly improve the out-of-band rejection and isolation between passbands.

Description

Technical Field

[0001] The present invention belongs to the field of electromagnetic fields and microwave technologies, and particularly relates to the field of dual-band filter design. Specifically, it is a design method for an asymmetric dual-band filter based on a frequency-variable coupling structure. Background Art

[0002] In the design of modern microwave filters, transmission zeros are crucial for improving out-of-band rejection. Due to the adaptability of realizing various transmission zeros, cross-coupling structures are commonly used in the design of microwave filters. Compared with traditional filters, cross-coupled filters have many advantages such as small size, high efficiency, good out-of-band rejection, high rectangularity coefficient, and flexible design. However, due to the existence of multiple coupling paths, while generating transmission zeros, it also greatly increases the complexity of debugging and topological structure. In view of this defect, in recent years, frequency-variable coupling structures have attracted more and more attention. Filters designed using frequency-variable coupling structures can not only optimize the topological structure and realize in-line topological structures, but also independently control the position of transmission zeros and reduce the complexity of filter debugging.

[0003] In addition, in wireless communication, there is a trend to integrate multiple applications into a single system, which requires multi-band filters. Among them, dual-band filters are widely used in various communication systems due to their relatively simple design methods and debugging processes. To design a dual-band filter, usually two methods are adopted: 1) using a multi-mode resonator; 2) using frequency transformation synthesis. The second method is more flexible and simpler because it can realize filters with specific performances and can be achieved by techniques commonly used in single-band filter design.

[0004] Recently, some scholars have proposed to design an asymmetric dual-band filter using two different low-pass prototypes. This kind of filter can realize different passbands with different bandwidths, orders, and return losses. However, due to the existence of too many cross-coupling paths, this filter also has problems of being difficult to simulate and design. Summary of the Invention

[0005] In view of the above existing problems or deficiencies, to solve the problem that it is difficult to simulate and design due to too many cross-coupling paths in the design of existing asymmetric dual-band filters, the present invention provides a design method for an asymmetric dual-band filter based on a frequency-variable coupling structure. In addition to being able to generate an asymmetric dual-band filter based on two low-pass prototype functions, realizing different passbands with different bandwidths, orders, and return losses, it can also eliminate all cross-couplings of the filter, realize in-line topological structures, and simplify the difficulty of filter design and simulation.

[0006] A design method for an asymmetric dual-band filter based on a frequency-variable coupling structure (such as Figure 7), and the specific steps are as follows:

[0007] Step 1: Starting from the transmission zeros and reflection zeros of two low-pass prototypes, use the frequency transformation function to obtain the transmission zeros and reflection zeros of the asymmetric dual-band filter function. The frequency transformation function is:

[0008] S = S' / a1 + b1 / (S' - jZ 12 ), S' < Z 12

[0009] S = S' / a2 + b2 / (S' - jZ 12 ), Z 12 <S'

[0010] where the expressions for the unknown parameters a i and b i are:

[0011]

[0012]

[0013] In the above formula, S = jΩ, S' = jΩ', a1, b1, a2, and b2 are unknown variables; -∞, -1, 1, ∞ of the first low-pass prototype correspond to -∞, P L1 , P U1 , Z 12 in the Ω' domain in sequence; -∞, -1, 1, ∞ of the second low-pass prototype correspond to Z 12 , P L2 , P U2 , ∞ in the Ω' domain in sequence. The Ω domain is the normalized frequency domain of the low-pass prototype, the Ω' domain is the normalized frequency domain of the dual-band filter, the S domain is the normalized S domain of the low-pass prototype, the S' domain is the normalized S domain of the dual-band filter, P Li is the lower boundary of the i-th passband, P Ui is the upper boundary of the i-th passband, P L1 = -1, P U2 = 1, Z 12 is the transmission zero between the two passbands, P U1 <Z 12 <P L2 .

[0014] According to the corresponding relationship, determine the values of the transmission zero Z 12 between the two passbands, the upper boundary P U1 of the first passband, and the lower boundary P L2 of the second passband, so as to obtain the values of the unknown parameters a1, b1, a2, and b2, and then obtain the transmission zeros and reflection zeros of the asymmetric dual-band filter function.

[0015] Step 2: According to the design objective that the two asymmetric passbands have different return losses, adjust the position of Z until it meets the design specifications. 12

[0016] Step 3: On the basis of Step 2, obtain the S-parameters and the transverse coupling matrix M of the asymmetric dual-band filter according to the filter synthesis theory. trans

[0017] Step 4: Select a topological structure, convert the frequency-dependent coupling matrix with unknown parameters corresponding to the topological structure into a non-frequency-dependent coupling matrix M through matrix similarity transformation, and set the optimization objective function; finally, use the constrained nonlinear minimization function fmincon to optimize and obtain all the unknown parameters of the frequency-dependent coupling matrix. final

[0018] The asymmetric dual-band filter designed based on the frequency-dependent coupling structure in the present invention has the following advantages:

[0019] 1. The present invention applies the frequency-dependent coupling structure to the design of an asymmetric dual-band filter based on two low-pass prototype functions, uses the optimization method proposed in Step 4 to solve all the unknown parameters of the frequency-dependent coupling matrix corresponding to the topological structure, eliminates the original cross-coupling paths, and the designed transmission zeros can be generated and independently controlled by the frequency-dependent coupling structure, further simplifying the topological structure of the filter and reducing the complexity of debugging.

[0020] 2. Compared with the traditional design of dual-band filters according to the frequency transformation method, the dual-band filter designed in the present invention converts two low-pass prototypes instead of one into a filter in Step 1, synthesizing an asymmetric dual-band filter. Different-order, return-loss, and bandwidth dual-band filters can be synthesized in different passbands and specified transmission zeros. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 is a schematic diagram of frequency transformation of the asymmetric frequency-dependent dual-band filter of the present invention;

[0022] Figure 2 is a schematic diagram of S-parameters obtained from the theoretical polynomial of the asymmetric frequency-dependent dual-band filter in the embodiment;

[0023] Figure 3 is the transverse matrix M of the asymmetric frequency-dependent dual-band filter in the embodiment; trans

[0024] Figure 4 is the frequency-dependent coupling topological structure in the embodiment;

[0025] Figure 5 is a schematic diagram of S-parameters of the frequency-dependent coupling matrix optimized in the embodiment; ​​​​

[0026] Figure 6 is the frequency - variable coupling matrix of the asymmetric frequency - variable double - passband filter in the embodiment;

[0027] Figure 7 is the flow chart of the present invention. Specific embodiments

[0028] The following further explains the content of the present invention in combination with the embodiments and the appended Figure 1-7 drawings.

[0029] First, the schematic diagram of frequency transformation in this embodiment is as Figure 1 shown. The Ω domain is the normalized frequency domain of the low - pass prototype, and the Ω' domain is the normalized frequency domain of the double - passband filter, where P L1 = - 1 and P U2 = 1. The first low - pass prototype in the Ω domain is converted to (-∞, Z 12 ) in the Ω' domain, and the second low - pass prototype in the Ω domain is converted to (Z 12 , ∞) in the Ω' domain, P U1 <Z 12 <P L2 .

[0030] The design objectives of the double - passband filter are as follows: The order of the first passband is two - order, and the return loss is greater than 15 dB. The order of the second passband is three - order, and the return loss is greater than 20 dB. The normalized bandwidths of the two passbands are (-1, - 0.7) and (0.55, 1) respectively, Ω' TZ = 3.02, Z 12 = 0.08. It can be calculated that a1 = 0.2871, b1 = 2.6818, a2 = 0.4759, b2 = 1.0132. Now, according to the synthesis theory of the filter and the frequency - transformation formula, the reflection zeros of the double - passband filter can be obtained, and thus the S - parameters and the transverse coupling matrix M trans can be obtained.

[0031] The passband width of the asymmetric double - passband filter to be designed is 100 MHz, the center frequency is 1950 MHz, and the three transmission zeros are 2107 MHz, 1954 MHz, and 1954 MHz respectively. The bandwidth of the first passband is 1900 MHz - 1915 MHz; the bandwidth of the second passband is 1977.5 MHz - 2000 MHz. The schematic diagram of its S - parameters is as Figure 2 shown, and the transverse coupling matrix is as Figure 3 shown.

[0032] Finally, on the basis of having obtained the transverse coupling matrix of the double - passband filter, the synthesis of the frequency - variable coupling matrix is carried out, and the selected topological structure is as Figure 4As shown, the three transmission zeros are respectively controlled and formed by the frequency-varying coupling between cavity 1 and cavity 2, the frequency-varying coupling between cavity 2 and cavity 3, and the frequency-varying coupling between cavity 3 and cavity 4. Then, the frequency-varying coupling matrix is converted into a non-frequency-varying coupling matrix M through matrix similarity transformation. final 。

[0033] The objective function of the optimization method is Cost = (λ trans - λ final ) T (λ trans - λ final ), where λ final corresponds to the eigenvalue related to the coupling matrix M after matrix transformation, final λ trans corresponds to the eigenvalue related to the transverse coupling matrix M trans , and T is the transpose symbol. Among them, is the eigenvalue of the transverse coupling matrix; is the eigenvalue corresponding to the matrix formed by the remaining elements after deleting the first row, the first column, the last row, and the last column of the transverse coupling matrix; is the eigenvalue corresponding to the matrix formed by the remaining elements after deleting the first row and the first column of the transverse coupling matrix; is the eigenvalue corresponding to the matrix formed by the remaining elements after deleting the last row and the last column of the transverse coupling matrix. The elements of λ final have the same meaning as the corresponding elements of λ trans .

[0034] For the above objective function, the constrained nonlinear minimization function fmincon is applied for optimization, and the frequency-varying coupling matrix of the specified topological structure can be obtained, and the error of the objective function is less than 1 * 10 - 10 . After obtaining the asymmetric double-passband frequency-varying coupling matrix as shown in Figure 6 , by applying the classical coupling matrix synthesis method, the S-parameters as shown in Figure 5 can be obtained.

[0035] From the above embodiments, it can be seen that when the present invention performs the synthesis of an asymmetric frequency-varying double-passband filter based on two low-pass prototype functions, the optimization result is in good agreement with the theoretical polynomial response.

[0036] The present invention applies a frequency-varying coupling structure to the design of an asymmetric dual-band filter based on two low-pass prototype functions. After converting the frequency-varying coupling matrix corresponding to the topological structure into a non-frequency-varying coupling matrix, all unknown parameters of the frequency-varying coupling matrix are optimized and solved through a constrained non-linear minimization function, thereby eliminating the original cross-coupling paths. The N-1 transmission zeros generated can be generated and independently controlled by the frequency-varying coupling structure, simplifying the topological structure of the filter and reducing the complexity of debugging, where N is the order of the filter. The present invention can synthesize dual-band filters with different orders, return losses, and bandwidths in different passbands and specified transmission zeros, realize an in-line topological structure, simplify the difficulty of filter design and simulation, and greatly improve the out-of-band rejection and the isolation degree between passbands. The present invention provides a good optimization effect for engineering practice and has important engineering value.

Claims

1. A design method for an asymmetric dual-band filter based on a frequency-variable coupling structure, characterized in that Including the following steps: Step 1, starting from the transmission zeros and reflection zeros of two low-pass prototypes, obtaining the transmission zeros and reflection zeros of the asymmetric dual-band filter function by using the frequency transformation function; the frequency transformation function is: S = S' / a1 + b1 / (S' - jZ 12 ), S' < Z 12 S = S' / a^2 + b^2 / (S' - jZ 12 ), Z 12 <S' where the unknown parameters a i and b i are expressed as: In the above formula, S = jΩ, S' = jΩ', a1, b1, a2, b2 are unknown variables; -∞, -1, 1, ∞ of the first low-pass prototype correspond to -∞, P L1 , P U1 , Z 12 ; -∞, -1, 1, ∞ of the second low-pass prototype correspond to Z 12 , P L2 , P U2 , ∞ in the Ω' domain; the Ω domain is the normalized frequency domain of the low-pass prototype, the Ω' domain is the normalized frequency domain of the double-passband filter, the S domain is the normalized S domain of the low-pass prototype, the S' domain is the normalized S domain of the double-passband filter, P Li is the lower boundary of the i-th passband, P Ui is the upper boundary of the i-th passband, P L1 = -1, P U2 = 1, Z 12 is the transmission zero between the two passbands, P U1 <Z 12 <P L2 ; Determine the transmission zero Z between two passbands according to the corresponding relationship 12 and the upper boundary P of the first passband U1 and the lower boundary P of the second passband L2 values, so as to obtain the values of the unknown parameters a1, b1, a2, b2, and then obtain the transmission zeros and reflection zeros of the asymmetric double-passband filter function; Step 2. Adjust the position of Z according to the design objective that the two asymmetric passbands have different return losses until it meets the design specifications; 12 ​ Step 3: On the basis of Step 2, obtain the S-parameters and the transverse coupling matrix M of the asymmetric dual-band filter according to the filter synthesis theory trans ; Step 4: Select a topological structure, and convert the frequency-varying coupling matrix with unknown parameters corresponding to the topological structure into a non-frequency-varying coupling matrix M through matrix similarity transformation final , and set the optimization objective function; finally, use the constrained nonlinear minimization function fmincon to optimize and obtain all unknown parameters of the frequency-varying coupling matrix.

2. The design method of the asymmetric dual-band filter based on the frequency-variable coupling structure according to claim 1, wherein: In step 4, the optimization objective function is Cost = (λ trans - λ final ) T (λ trans - λ final ), where λ final corresponds to the eigenvalue related to the coupled matrix M final after matrix transformation, and λ trans corresponds to the eigenvalue related to the transverse coupling matrix M trans , and T is the transpose symbol; where is the eigenvalue of the transverse coupling matrix; is the eigenvalue corresponding to the matrix formed by the remaining elements after deleting the first row, the first column, the last row, and the last column of the transverse coupling matrix; is the eigenvalue corresponding to the matrix formed by the remaining elements after deleting the first row and the first column of the transverse coupling matrix; is the eigenvalue corresponding to the matrix formed by the remaining elements after deleting the last row and the last column of the transverse coupling matrix; The elements of λ final have the same meaning as the corresponding elements of λ trans .

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