A coupling matrix design method for multi-passband filters with preset out-of-band transmission zeros

Abstract

The present invention relates to the technical field of communication equipment components, and discloses a multi-passband filter coupling matrix design method capable of presetting out-of-band transmission zeros, comprising the following steps: converting a normalized frequency band in a low-pass prototype filter into upper and lower limit channel indicators of a multi-channel filter; designing a bandpass portion in a multi-passband filter coupling matrix; calculating a bandstop portion in a multi-passband filter coupling matrix; and generating an overall coupling matrix according to the bandpass portion and the bandstop portion in the multi-passband filter coupling matrix. The present invention can map the response of a low-pass prototype filter into an actual frequency domain, mapping it into a multi-passband filter, and is applicable to any type of resonator. Theoretically, any number of passbands and a customized bandwidth of each passband can be realized. Compared with the frequency mapping theory that has been proposed, it can realize the precise presetting of out-of-band transmission zeros, and can well improve the out-of-band suppression performance.

Description

Technical Field

[0001] The present invention relates to the technical field of communication equipment components, and in particular to a design method for a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero point. Background Art

[0002] In the field of modern communications, the application frequency bands of various communication systems are concentrated in the low frequency bands of radio frequency and microwave bands, which makes the spectrum resources very crowded. In the past, single-band communication systems could hardly meet the various requirements of modern communications. To solve this problem, in addition to developing the application frequency band to a higher frequency band, it is also possible to combine cross-coupling and other technologies to design a multi-band filter with higher performance to meet the trend and demand of multi-frequency and integrated communication systems, and avoid interference between adjacent channels. In recent years, many scholars have conducted in-depth research on the design theory and methods of multi-band filters. Specifically summarized as follows:

[0003] Method 1: Use the high harmonics of multi-mode resonators to form multiple passbands. This design method can reduce the number of resonators and greatly reduce the size of the filter. However, this method requires individual control of the resonant frequencies of the multi-mode resonators, the coupling of each passband resonant mode, and the input / output coupling amount of each passband. Generally, it is not easy to achieve high isolation between passbands using this method, especially when the passbands are closely spaced from each other.

[0004] Method 2: Form a multi-band filter by connecting multiple bandpass filters in parallel. This method first requires designing multiple bandpass filters separately and then connecting them in parallel. After that, a complex design process is required for the matching circuits between the multiple bandpass filters, which will bring additional insertion loss and design time.

[0005] Method 3: Comprehensive methods represented by frequency mapping, coupling matrix, etc. With the deepening of research, these comprehensive methods have gradually matured. Relevant scholars have given a frequency transformation method for dual-passband and triple-passband filters based on coupling matrix synthesis. This theory is based on the normalized low-pass prototype. After two steps of frequency mapping, the multi-passband prototype filter and the transmission zero and reflection zero are obtained. The dual-passband characteristic function is obtained, and then the corresponding coupling matrix is ​​obtained. This method is designed based on the position distribution of zero poles, so the out-of-band transmission zero can be preset. In recent years, a different method has been proposed to design multi-passband filters by connecting band-stop resonators to bandpass resonators. The bandpass resonator is used to form the initial single-band frequency response, while the bandstop resonator is used to introduce a stopband in the passband. Among them, different coupling topologies can be formed by different connection methods, such as the "star" topology, which is formed by directly connecting all bandstop resonators to the bandpass resonator. This "star" topology is usually only suitable for the design of multi-passband microstrip filters due to physical structural limitations. Another commonly used topology is to cascade band-stop resonators of different stopbands in sequence and then connect them to a bandpass resonator. This coupling topology is applicable to all types of filters, whether microstrip, coaxial, substrate-integrated waveguide or dielectric waveguide.

[0006] However, the representatives of existing frequency mapping technologies mainly have the following defects or shortcomings:

[0007] Method 1 is a frequency conversion method represented by finding the positions of zeros and poles of multi-passband filters. Although this method can accurately preset the transmission zeros, it requires two-step mapping, the calculation process is very cumbersome, and the coupling between each resonator is also very complex, making the optimization process very difficult.

[0008] The second method is the frequency mapping method based on the "star" topology. This method only requires one step of mapping, but it is generally only applicable to multi-passband microstrip filters. If it is other types of filters, such as waveguide filters, the number of passbands will be limited due to the physical structure. In the existing research on this method, there is no detailed description of the preset out-of-band transmission zero point, and the calculation process of the coupling matrix is ​​not detailed enough.

[0009] Method 3 is a frequency mapping method based on cascade topology. This method only requires one step of mapping and has no design restrictions on the physical structure. However, existing research cannot accurately preset the out-of-band transmission zero point.

[0010] In summary, the design method based on the frequency mapping function can theoretically realize any number of passbands and different passband bandwidths, but there is no complete research on the precise preset and adjustment of the out-of-band transmission zero point. Based on this, the present invention proposes a method for calculating the coupling matrix of a multi-passband filter that can accurately preset the out-of-band transmission zero point. Summary of the invention

[0011] In view of the problems in the related art, the present invention proposes a multi-passband filter coupling matrix design method capable of presetting out-of-band transmission zero points, so as to overcome the above technical problems existing in the existing related art.

[0012] To this end, the specific technical solution adopted by the present invention is as follows:

[0013] A method for designing a coupling matrix of a multi-passband filter capable of presetting an out-of-band transmission zero point comprises the following steps:

[0014] S1, converting the normalized frequency band in the low-pass prototype filter into the upper and lower limit channel indicators of the multi-channel filter, and calculating the frequency mapping function;

[0015] S2, designing the bandpass part in the coupling matrix of the multi-passband filter according to the calculated frequency mapping function combined with the out-of-band transmission zero point;

[0016] S3, calculating the band-stop part in the coupling matrix of the multi-passband filter according to the frequency mapping function;

[0017] S4. Generate an overall coupling matrix according to the bandpass part and the bandstop part in the multi-passband filter coupling matrix.

[0018] Further, the conversion of the normalized frequency band in the low-pass prototype filter into the upper and lower limit channel indicators of the multi-channel filter includes:

[0019] The normalized frequency band (-1, +1) in the Ω domain of the low-pass prototype filter is converted into the upper and lower passband indexes of the multi-passband filter, and n passbands (ω L1 ,ω H1 ), (ω L2 ,ω H2 ),…,(ω Ln ,ω Hn ), where ω L1 ,ω L2 ,…,ω Ln Represents the lower frequency of each passband, ω H1 ,ω H2 ,…,ω Hn Represent the upper frequency of each passband respectively.

[0020] Furthermore, the calculation formula of the frequency mapping function is:

[0021]

[0022] Where Ω represents the normalized angular frequency of the low-pass prototype filter; ω represents the actual angular frequency of the multi-passband filter; T (n) (ω) represents the frequency mapping function; ω01 ,ω 02 ,…,ω 0n They correspond to the resonant frequencies of the n resonators respectively; b1, b2, ..., b n They correspond to the susceptance slopes of the n resonators respectively.

[0023] Furthermore, since the normalized frequency band (-1, +1) in the Ω domain is mapped to n passbands (ω L1 ,ω H1 ), (ω L2 ,ω H2 ),…,(ω Ln ,ω Hn ), we get the following 2n equations:

[0024]

[0025] Where, T (n) (ω H1 ), T (n) (ω H2 ),…,T (n) (ω Hn ) represent the low-pass prototype angular frequency after the upper frequency of each passband is substituted into the frequency mapping formula, and its value is 1; T (n) (ω L1 ), T (n) (ω L2 ),…,T (n) (ω Ln ) represent the low-pass prototype angular frequencies after the lower frequency of each passband is substituted into the frequency mapping formula, and their values ​​are -1.

[0026] Further, the design of the bandpass part in the multi-passband filter coupling matrix according to the calculated frequency mapping function combined with the out-of-band transmission zero point includes:

[0027] The frequency of the out-of-band transmission zero point is mapped to a mapping frequency according to the calculated frequency mapping function to obtain the mapping frequency of the out-of-band transmission zero point; and the coupling coefficient of the initial bandpass response is calculated.

[0028] Furthermore, the calculation formula for the center frequency of the initial bandpass response is:

[0029]

[0030] The relationship between the initial resonator's susceptance slope b1 and the relative bandwidth FBW is:

[0031]

[0032] In the formula, ω 01represents the resonant frequency of the initial resonator; BW1, BW2, ... BW n They represent the bandwidths of the 1st passband, the 2nd passband, … the nth passband respectively; BW represents the total bandwidth of all passbands.

[0033] Further, the calculating of the band-stop part in the multi-passband filter coupling matrix according to the frequency mapping function includes:

[0034] Based on the frequency mapping function, the coupling coefficients between adjacent band-stop resonators and the self-coupling coefficients of the band-stop resonators are calculated.

[0035] Furthermore, the calculation formula is:

[0036]

[0037] Where i = 2, 3, ..., n and j = 1, 2, 3, ..., N, represents the coupling matrix value between each resonator except the bandpass filter; represents the coupling coefficient between each resonator except the bandpass filter; represents the self-coupling matrix value of the band-stop resonator; represents the self-coupling coefficient of the band-stop resonator.

[0038] The beneficial effects of the present invention are as follows: the present invention can map the response of the low-pass prototype filter into the actual frequency domain and map it into a multi-passband filter, which is suitable for any type of resonator and can theoretically achieve any number of passbands and a customized bandwidth of each passband. The coupling matrix calculation process proposed in the present invention can all be calculated through the frequency mapping function, which is more convenient and flexible, and the proposed calculation method is more general and more instructive. Not only that, compared with the frequency mapping theory that has been proposed, it can achieve accurate preset of the out-of-band transmission zero point, which can greatly improve the out-of-band suppression performance. The present invention also designs a dual-passband dielectric waveguide filter with a CQ coupling topology to verify the proposed theory. Compared with the traditional dielectric waveguide filter, the present invention realizes a filter with multiple passbands and multiple transmission zero points, and the out-of-band suppression controllability is better. BRIEF DESCRIPTION OF THE DRAWINGS

[0039] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0040] Figure 1is a flow chart of a method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero point according to an embodiment of the present invention;

[0041] Figure 2 is a schematic diagram of frequency mapping transformation from a low-pass prototype frequency response in the Ω domain to an n-passband frequency response in the ω domain in an embodiment of the present invention;

[0042] Figure 3 Schematic diagram of mapping transformation from the parallel capacitor of the low-pass prototype in the Ω domain to n resonant units in the ω domain in an embodiment of the present invention;

[0043] Figure 4 Schematic diagram of a general coupling topology of an n-passband N-order bandpass filter in an embodiment of the present invention;

[0044] Figure 5 1 is a schematic diagram of the principle of a method for designing a coupling matrix of a multi-passband filter capable of presetting an out-of-band transmission zero point according to an embodiment of the present invention;

[0045] Figure 6 is a schematic diagram of theoretical S parameters generated according to an embodiment of the present invention;

[0046] Figure 7 is a three-dimensional structural diagram of a dielectric waveguide filter having a CQ according to an embodiment of the present invention;

[0047] Figure 8 is a coupling topology diagram of a dielectric waveguide filter having a CQ according to an embodiment of the present invention;

[0048] Fig. 9 Schematic diagram of theoretical, simulation and measurement results of a dual-passband dielectric waveguide filter with one CQ according to an embodiment of the present invention. DETAILED DESCRIPTION

[0049] To further illustrate each embodiment, the present invention provides drawings, which are part of the disclosure of the present invention and are mainly used to illustrate the embodiments and can be used in conjunction with the relevant descriptions in the specification to explain the operating principles of the embodiments. With reference to these contents, ordinary technicians in the field should be able to understand other possible implementations and advantages of the present invention. The components in the figures are not drawn to scale, and similar component symbols are generally used to represent similar components.

[0050] According to an embodiment of the present invention, a method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero point is provided.

[0051] The present invention is further described with reference to the accompanying drawings and specific embodiments. Figure 1-Figure 8 As shown, according to an embodiment of the present invention, a method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero point comprises the following steps:

[0052] S1, converting the normalized frequency band in the low-pass prototype filter into the upper and lower limit channel indicators of the multi-channel filter, and calculating the frequency mapping function;

[0053] like Figure 2 As shown, the normalized frequency band (-1, +1) in the Ω domain of the low-pass prototype is converted into the upper and lower passband indicators of the multi-passband filter, that is, (ω L1 ,ω H1 ), (ω L2 ,ω H2 ),…,(ω Ln ,ω Hn ), where ω L1 ,ω L2 ,…,ω Ln Represents the lower frequency of each passband, ω H1 ,ω H2 ,…,ω Hn Represents the upper frequency of each passband. For the transformation of frequency mapping, the relationship between the normalized low-pass prototype and the n-passband filter is:

[0054]

[0055] Where Ω represents the normalized angular frequency of the low-pass prototype filter; ω represents the actual angular frequency of the multi-passband filter; T (n) (ω) represents the frequency mapping function; parameter ω 01 ,ω 02 ,…,ω 0n , b1, b2, …, b n are 2n unknown constants in the frequency mapping function. Since the normalized frequency band (-1, +1) in the Ω domain needs to be mapped to n passbands (ω) in the ω domain according to the frequency mapping function L1 ,ω H1 ), (ω L2 ,ω H2 ),…,(ω Ln ,ω Hn ), so we can get the following 2n equations:

[0056]

[0057] Where, T (n) (ω H1 ), T (n) (ω H2 ),…,T (n) (ω Hn ) represent the low-pass prototype angular frequency after the upper frequency of each passband is substituted into the frequency mapping formula, and its value is 1; T (n) (ωL1 ), T (n) (ω L2 ),…,T (n) (ω Ln ) represent the low-pass prototype angular frequencies after the lower frequency of each passband is substituted into the frequency mapping formula, and their values ​​are -1.

[0058] Therefore, the 2n unknown constants can be determined by solving the above 2n equations. Figure 3 The figure shows the transformation from the shunt capacitor of the low-pass prototype in the Ω domain to n resonant units in the ω domain. The n resonant units can be realized by cascading n resonators. In this way, the 2n unknown constants have their own physical meaning: ω 01 ,ω 02 ,…,ω 0n Corresponding to the resonant frequencies of n resonators; b1, b2, ..., b n is the susceptance slope of the n resonators. From a functional point of view, the first resonator (ω 01 ,b1) act as bandpass resonators, producing an initial bandpass response. The remaining resonators act as bandstop resonators, generating n-1 stopbands within the initial passband and dividing it into n passbands. Therefore, a general coupling scheme for an n-passband N-order bandpass filter can be constructed by using n resonant units, such as Figure 4 As shown, the corresponding coupling matrix is ​​as follows:

[0059]

[0060] S2, designing the bandpass part in the coupling matrix of the multi-passband filter according to the calculated frequency mapping function combined with the out-of-band transmission zero point;

[0061] Wherein, the design of the bandpass part in the multi-passband filter coupling matrix according to the calculated frequency mapping function combined with the out-of-band transmission zero point includes:

[0062] The out-of-band transmission zero (ω TZ1 ,ω TZ2 …,ω TZK )(K≤N) is mapped to the frequency (Ω TZ1 ,Ω TZ2 …,Ω TZK ), and the mapping frequency of the out-of-band transmission zero point is obtained, where ω TZ1 ,ω TZ2 …,ω TZK Respectively represent the angular frequency of the out-of-band transmission zero point in the frequency response of the multi-passband filter; Ω TZ1 ,Ω TZ2 …,Ω TZKThey represent the normalized angular frequencies of the transmission zeros in the frequency response of the low-pass prototype filter respectively;

[0063] Calculate the coupling coefficient of the initial bandpass response. The center frequency of the initial bandpass response is ω 01 / 2π. In the calculation process of formula (2), the relationship between b1 and relative bandwidth (FBW) is obtained:

[0064]

[0065] In the formula, ω 01 represents the resonant frequency of the initial resonator; BW1, BW2, ... BW n They represent the bandwidths of the 1st passband, the 2nd passband, … the nth passband respectively; BW represents the total bandwidth of all passbands.

[0066] Therefore, the bandwidth of the initial passband response is the sum of the bandwidths of all n passbands, and the FBW is equal to 1 / b1. By using the traditional design method of a single passband filter, the center frequency of ω 01 The initial bandpass response of / 2π and FBW of 1 / b1 is synthesized together with the mapped frequency of the transmission zero point and the required in-band return loss into the coupling coefficient between the N bandpass resonators.

[0067] S3, calculating the band-stop part in the coupling matrix of the multi-passband filter according to the frequency mapping function;

[0068] The step of calculating the band-stop part in the multi-passband filter coupling matrix according to the frequency mapping function comprises:

[0069] Based on the frequency mapping function, the coupling coefficient between adjacent band-stop resonators and the self-coupling coefficient of the band-stop resonator are calculated. The calculation formula is:

[0070]

[0071] Where i = 2, 3, ..., n and j = 1, 2, 3, ..., N, represents the coupling matrix value between each resonator except the bandpass filter; represents the coupling coefficient between each resonator except the bandpass filter; represents the self-coupling matrix value of the band-stop resonator; represents the self-coupling coefficient of the band-stop resonator.

[0072] S4. Generate an overall coupling matrix according to the bandpass part and the bandstop part in the multi-passband filter coupling matrix.

[0073] Specifically, the coupling coefficients calculated above can be used to construct a normalized coupling matrix. Except for the coupling coefficients mentioned above, the rest are all zero.

[0074] In order to better understand the above technical solution of the present invention, this embodiment also proposes a dual-passband dielectric waveguide filter with a CQ structure, and its specific generation process is as follows:

[0075] Step 1: Determine the specific indicators of the dual-passband filter;

[0076] Passband 1: 3.30GHz-3.35GHz (bandwidth: 0.05GHz);

[0077] Passband 2: 3.38GHz-3.45GHz (bandwidth: 0.07GHz);

[0078] In-band return loss: 20dB;

[0079] Out-of-band transmission zero position: 3.24GHZ, 3.51GHz;

[0080] In the second step, the frequency mapping function calculated according to the bandwidth of the two passbands is:

[0081]

[0082] Therefore, the center frequency and bandwidth of the initial bandpass response can be calculated:

[0083]

[0084] BW=0.05+0.07=0.12GHz

[0085] The third step is to substitute the position of the out-of-band transmission zero point into the frequency mapping function to obtain:

[0086] Ω TZ1 =-2.2

[0087] Ω TZ2 =2.2

[0088] The fourth step is to calculate the coupling coefficient of the initial bandpass response based on this, and its coupling matrix is:

[0089]

[0090] Other key coupling coefficients are derived from the following equations:

[0091]

[0092] Step 5. The overall coupling matrix of the final dual-passband filter is:

[0093]

[0094] The S parameters of the coupling matrix are as follows: Figure 6As shown. Figure 6 It can be seen that the theoretical S parameters generated by this method are completely consistent with the target indicators.

[0095] The next step is to simulate and measure the dual-passband filter. The dielectric structure is as follows: Figure 7 As shown. The dielectric block can be made of dielectric ceramic material by firing. Except for the rings 41 and 42, the remaining surfaces are all metallized. Blind hole 11 is used to adjust the frequency of resonator R1, blind hole 12 is used to adjust the frequency of resonator R2, blind hole 13 is used to adjust the frequency of resonator R3, blind hole 14 is used to adjust the frequency of resonator R4, and blind hole 15 is used to adjust the frequency of resonator R1. (2) The blind hole 16 is used to adjust the resonator R2 (2) The blind hole 17 is used to adjust the resonator R3 (2) The blind hole 18 is used to adjust the resonator R4 (2) frequency; blind hole 21 is used to adjust the coupling coefficient between resonators R1 and R2, blind hole 22 is used to adjust the coupling coefficient between resonators R2 and R3, blind hole 23 is used to adjust the coupling coefficient between resonators R3 and R4, blind hole 24 is used to adjust the coupling coefficient between resonators R1 and R4, blind hole 25 is used to adjust the coupling coefficient between resonators R1 and R1 (2) The blind hole 26 is used to adjust the coupling coefficient between resonators R2 and R2 (2) The blind hole 27 is used to adjust the coupling coefficient between resonators R3 and R3 (2) The blind hole 28 is used to adjust the coupling coefficient between resonators R4 and R4 (2) The coupling coefficient between them; these blind holes are all on the lower surface of the dielectric block. The upper surface of resonator R1 is provided with a feeding blind hole 31 and an unmetallized ring 41; the upper surface of resonator R4 is provided with a feeding blind hole 32 and an unmetallized ring 42. Resonator R1 (2) and R2 (2) The coupling window 51 and resonator R3 (2) and R4 (2) The coupling window 61 between the two is set to prevent the dielectric waveguide filter from being severely deformed during the cooling process after firing, but its coupling coefficient is very small and has little effect on the filter performance and can be ignored. Figure 8 shown.

[0096] In the above embodiment, the physical dimensions of the dielectric part of the dual-passband filter are 32.0 mm × 52.0 mm × 6 mm, i.e., 0.359λ0 × 0.584λ0 × 0.067λ0, where λ0 is the free space wavelength at the center frequency in vacuum. The results of synthesis, simulation and measurement are given in Fig. 9The comparison was made in , where good agreement was observed. The measurement results show that the minimum insertion loss of the first passband is about 0.86dB and the return loss is greater than 16.0dB. The minimum insertion loss of the second passband is about 0.83dB and the return loss is greater than 16.4dB. Two out-of-band transmission zeros are introduced at 3.25GHz and 3.51GHz respectively.

[0097] The above design examples show that the proposed design method of the multi-passband dielectric waveguide filter has a simple process, specific calculation, and can accurately preset the out-of-band transmission zero point. The dielectric waveguide filter designed by the present invention has high feasibility and practicality, and works within the main frequency band of China Telecom.

[0098] In summary, compared with other synthesis methods, the frequency mapping technology in the method of this embodiment is an excellent choice for synthesizing multi-passband filters with near passbands. The main process of the frequency mapping method of the present invention is to map the ideal low-pass prototype filter response to the upper and lower passband indicators of multiple passbands through a frequency mapping function. The frequency mapping function used is essentially to cascade multiple band-stop resonators to the bandpass resonator in sequence, and design the bandpass part in the multi-passband filter coupling matrix based on the calculated frequency mapping function and the out-of-band transmission zero point, so as to achieve the preset out-of-band transmission zero point; then calculate the band-stop part in the multi-passband filter coupling matrix according to the relevant coefficients in the frequency mapping function, and finally generate the overall coupling matrix, and this method discusses the generation process of the n-passband filter coupling matrix, which is more general and instructive. In the design example, a dual-passband dielectric waveguide filter with a CQ coupling topology is designed. Due to the use of the CQ coupling topology and the dielectric waveguide resonator, this filter has the advantages of dual passband, low loss and high out-of-band suppression.

[0099] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero, characterized in that: The following steps are involved: S1, converting the normalized frequency band in the low-pass prototype filter into the upper and lower limit channel indicators of the multi-channel filter, and calculating the frequency mapping function; S2, designing the bandpass part in the coupling matrix of the multi-passband filter according to the calculated frequency mapping function combined with the out-of-band transmission zero point; S3, calculating the band-stop part in the coupling matrix of the multi-passband filter according to the frequency mapping function; S4, generating an overall coupling matrix according to the bandpass part and the bandstop part in the multi-passband filter coupling matrix; The process of converting the normalized frequency band in the low-pass prototype filter into the upper and lower limit channel indicators of the multi-channel filter comprises: The normalized frequency band (-1, +1) in the Ω domain of the low-pass prototype filter is converted into the upper and lower passband indexes of the multi-passband filter, and n passbands (ω L1 ,ω H1 ), (ω L2 ,ω H2 ),…,(ω Ln ,ω Hn ), where ω L1 ,ω L2 ,…,ω Ln Represents the lower frequency of each passband, ω H1 ,ω H2 ,…,ω Hn The upper frequency of each passband respectively; The design of the bandpass part in the multi-passband filter coupling matrix according to the calculated frequency mapping function combined with the out-of-band transmission zero point includes: According to the calculated frequency mapping function, the frequency of the out-of-band transmission zero point is mapped to a mapping frequency to obtain the mapping frequency of the out-of-band transmission zero point; and the coupling coefficient of the initial bandpass response is calculated; The center frequency of the initial bandpass response is given by: The relationship between the initial resonator's susceptance slope b1 and the relative bandwidth FBW is: In the formula, ω 01 represents the resonant frequency of the initial resonator; BW1, BW2, ...BW n They represent the bandwidths of the first passband, the second passband, … the nth passband respectively; BW is the total bandwidth of all passbands.

2. The method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero according to claim 1, characterized in that: The calculation formula of the frequency mapping function is: Where, Ω represents the normalized angular frequency of the low-pass prototype filter; ω represents the actual angular frequency of the multi-passband filter; T (n) (ω) represents the frequency mapping function; ω 01 ,ω 02 ,…,ω 0n They correspond to the resonant frequencies of n resonators respectively; b1, b2, …, b n They correspond to the susceptance slopes of the n resonators respectively.

3. The method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero according to claim 2, characterized in that: Since the normalized frequency band (-1, +1) in the Ω domain is mapped to n passbands (ω L1 ,ω H1 ), (ω L2 ,ω H2 ),…,(ω Ln ,ω Hn ), we get the following 2n equations: Where, T (n) (ω H1 ), T (n) (ω H2 ),…,T (n) (ω Hn ) represent the low-pass prototype angular frequencies after the upper frequency of each passband is substituted into the frequency mapping formula; T (n) (ω L1 ), T (n) (ω L2 ),…,T (n) (ω Ln ) represent the low-pass prototype angular frequencies after the lower frequency of each passband is substituted into the frequency mapping formula.

4. The method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero according to claim 1, characterized in that: Calculating the band-stop part in the multi-passband filter coupling matrix according to the frequency mapping function comprises: Based on the frequency mapping function, the coupling coefficients between adjacent band-stop resonators and the self-coupling coefficients of the band-stop resonators are calculated.

5. The method for designing a multi-passband filter coupling matrix capable of presetting an out-of-band transmission zero according to claim 4, characterized in that: The calculation formula is: Where i = 2, 3, ..., n and j = 1, 2, 3, ..., N; represents the coupling matrix value between each resonator except the bandpass filter; represents the coupling coefficient between each resonator except the bandpass filter; represents the self-coupling matrix value of the band-stop resonator; represents the self-coupling coefficient of the band-stop resonator.

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