Broadband microwave filter and implementation method thereof

Abstract

The invention discloses a broadband microwave filter and an implementation method thereof, and a prototype circuit of the broadband microwave filter with a plurality of transmission zeros of a lumped parameter element circuit topological structure is obtained by constructing a transmission zeros by adopting a generalized pole extraction comprehensive method to implement a complex function. And obtaining a circuit structure of the broadband microwave filter through circuit conversion and microwave circuit distribution parameter element equivalent replacement, continuously performing impedance conversion on a distributed element circuit topological structure by using an impedance conversion method, reducing the characteristic impedance of a transmission line, and obtaining the final broadband microwave filter. The invention further designs a medium-bandwidth microwave filter which is composed of four LC resonators connected in series, three LC resonator branches and three susceptance elements connected in parallel. The broadband microwave filter with high selectivity can be designed, and the microstrip line has low characteristic impedance, so that the problem of performance deterioration of the filter caused by discontinuous impedance of the transmission line is reduced, and the working stability is improved.

Description

Technical Field

[0001] The present invention relates to the field of filters, in particular to a method for implementing a complex broadband microwave filter based on a transmission line with a standardized characteristic impedance, and a broadband microwave filter implemented by this method. Background Art

[0002] In modern wireless communication, radar systems, measuring instruments, and other microwave applications, filters play a crucial role. Among them, broadband filters are widely used in military radars and wireless communications due to their strong anti-interference ability, fast transmission speed, large system capacity, etc. As a key component in broadband systems, broadband filters have always been a research hotspot. With the improvement of system integration, filters not only require miniaturization in size but also need to simultaneously meet requirements such as wide frequency band, low loss, and high selectivity. This often requires broadband filters to have a higher order and be able to arbitrarily specify the number and position of transmission zeros - that is, to achieve a complex response function, but it is particularly difficult for planar broadband filters.

[0003] Both wide bandwidth and high selectivity are important indicators for filters. In planar circuits, for existing broadband filter designs, it is a challenging task to arbitrarily specify the number and position of transmission zeros. Several methods for implementing broadband filters have been proposed in the existing literature, including optimal short-circuit stub filters, high-low pass (bandpass-bandstop) cascades, and multimode resonators.

[0004] To introduce zeros, the optimal short-circuit stub filter introduces cross-coupling at the input and output ports. However, the number and position of transmission zeros that can be introduced by this method are limited. In contrast, broadband filters based on multimode resonators achieve broadband response by reasonably controlling the distribution of multiple modes of the resonator in the passband. However, due to the simple structure of the resonator and the interlinkage between harmonics, it is difficult to accurately control the bandwidth, and it is also impossible to flexibly control the number and position of zeros.

[0005] In addition, when the passband frequency of the bandpass filter is in the C band, the comprehensively obtained capacitance or inductance values are usually large and difficult to implement. The traditional high-low impedance line design scheme cannot meet the requirements of high capacitance or inductance values, and extremely high characteristic impedance transmission lines cannot be realized by simple microstrip processes. Moreover, the larger the filter bandwidth, the stronger the coupling between resonators, and it is difficult to achieve in a planar structure. Usually, processing technologies with a multi-layer structure, such as LTCC technology, multi-layer LCP technology, etc., are required to achieve strong coupling. However, this also comes with higher processing costs and higher precision requirements.

[0006] In fact, in the field of traditional filter design, there are usually three basic design routes: one is the design based on the lumped parameter element model; the second is the design based on the distributed parameter element model; the third is the design based on the coupled resonator model. Among them, although the first and second routes can achieve broadband design, due to the adverse effects of parasitic parameters on the lumped parameter elements at frequencies above 2 GHz, it is impossible to design a high-frequency broadband filter. Although the design idea using distributed parameter elements helps to achieve broadband design, it is difficult to directly synthesize and flexibly construct complex transfer functions. As for the third solution based on coupled resonators, although it can achieve complex transfer functions, its design theory is only applicable to narrowband filters. Moreover, more importantly, the microstrip process is widely used because of its simple and convenient manufacturing and easy integration characteristics. In traditional methods, the extremely high-impedance microstrip lines of distributed elements bring extremely thin line widths, which have high requirements for the process. Summary of the Invention

[0007] The object of the present invention is to provide a broadband microwave filter and its implementation method to design a broadband microwave filter with high selectivity and high stability for all or part of the above-mentioned problems.

[0008] The technical solution adopted by the present invention is as follows:

[0009] An implementation method of a broadband microwave filter includes:

[0010] Construct transfer zeros through the generalized pole extraction synthesis method to realize complex functions, and obtain a prototype circuit of a broadband microwave filter with multiple transfer zeros constructed by lumped parameter elements;

[0011] Transform the circuit topology structure of the lumped parameter elements of the prototype circuit into the circuit topology structure of distributed parameter elements;

[0012] Perform impedance transformation on the circuit topology structure of distributed elements to reduce the characteristic impedance of the transmission line.

[0013] Further, in the circuit topology structure of the distributed parameter elements of the broadband microwave filter, multiple transfer zeros are introduced by the way of connecting multiple resonator stubs in parallel.

[0014] Further, among the multiple resonator stubs connected in parallel, in the resonator stub introducing the high-end transfer zero, the series LC resonator is realized by an open-circuit quarter-wavelength resonator; in the resonator stub introducing the low-end transfer zero, the inductor is realized by a high-impedance transmission line, and the capacitor is realized by a fan-shaped metal sheet.

[0015] Further, transforming the circuit topology structure of the lumped parameter elements of the prototype circuit into the circuit topology structure of distributed parameter elements includes:

[0016] Replace the series LC resonator with a half-wavelength resonator; replace the inductive element with a high-impedance transmission line; replace the grounded capacitor and the susceptance element that does not change with frequency with a fan-shaped metal sheet.

[0017] Further, the impedance transformation of the distributed parameter element circuit topology includes:

[0018] Convert the high-impedance transmission line in the distributed element circuit topology into a low-impedance transmission line;

[0019] Replace the lumped parameter elements in the converted circuit topology with distributed parameter elements.

[0020] Further, the conversion of the high-impedance transmission line in the distributed element circuit topology into a low-impedance transmission line includes:

[0021] Convert at least one section of the high-impedance transmission line in the distributed element circuit topology into two sections of low-impedance transmission lines, and introduce susceptance elements that do not change with frequency at both ends and in the middle of the two sections of low-impedance transmission lines.

[0022] Further, the process of converting the high-impedance transmission line into two sections of low-impedance transmission lines and introducing susceptance elements that do not change with frequency at both ends and in the middle of the two sections of low-impedance transmission lines includes:

[0023] Convert the high-impedance transmission line into two transition transmission lines with equal characteristic admittance and length;

[0024] Convert the two transition transmission lines into two sections of low-impedance transmission lines with equal characteristic admittance and length, and introduce susceptance elements that do not change with frequency at both ends and in the middle of the two sections of low-impedance transmission lines, and the susceptance elements at both ends are the same.

[0025] Further, the relationship between the high-impedance transmission line, the transition transmission line, the low-impedance transmission line, and the three susceptance elements is:

[0026] Y1 = kY0cscθ2 / cscθ1

[0027] B1 = Y1cotθ2 - Y0cotθ1

[0028] B2 = 2Y1cotθ2 - 2k 2 Y0cotθ1

[0029] B3 = Y1cotθ2 - Y0cotθ1

[0030] Among them, Y0 and Y1 are the characteristic admittances of the high-impedance transmission line and the low-impedance transmission line respectively, θ0, θ1, and θ2 are the transmission line lengths of the high-impedance transmission line, the transition transmission line, and the low-impedance transmission line respectively, B1 and B3 are the values of the susceptance elements at both ends, B2 is the value of the susceptance element in the middle, and k is the conversion coefficient.

[0031] The present invention also provides a medium-bandwidth microwave filter designed by using the implementation method of the above broadband microwave filter. The main path of the medium-bandwidth microwave filter includes 4 series LC resonators connected in series, 3 LC resonator stubs, and 3 shunt susceptance elements that do not change with frequency; the 3 LC resonator stubs are respectively connected between every two adjacent series LC resonators, and the 3 susceptance elements are respectively connected between every two adjacent series LC resonators.

[0032] Further, the first port of the medium-bandwidth microwave filter is sequentially connected to the first microstrip line section, the second microstrip line section, the third microstrip line section, the fourth microstrip line section, the fifth microstrip line section, the sixth microstrip line section, the seventh microstrip line section, the eighth microstrip line section, the ninth microstrip line section, the tenth microstrip line section, and the second port along the main path;

[0033] The upper end of the eleventh microstrip line section connected to the branch is connected to the connection between the first microstrip line and the second microstrip line, and the lower end is connected to the first sector-shaped metal disc; the upper end of the twelfth microstrip line section connected to the branch is connected to the connection between the second microstrip line and the third microstrip line; the upper end of the thirteenth microstrip line section connected to the branch is connected to the connection between the fourth microstrip line and the fifth microstrip line; the upper end of the fourteenth microstrip line section connected to the branch is connected to the connection between the fifth microstrip line and the sixth microstrip line; the lower end of the fifteenth microstrip line section connected to the branch is connected to the connection between the fifth microstrip line and the sixth microstrip line; the lower end of the sixteenth microstrip line section connected to the branch is connected to the connection between the sixth microstrip line and the seventh microstrip line; the lower end of the seventeenth microstrip line section connected to the branch is connected to the connection between the eighth microstrip line and the ninth microstrip line; the upper end of the eighteenth microstrip line section connected to the branch is connected to the connection between the ninth microstrip line and the tenth microstrip line, and the lower end is connected to the second sector-shaped metal disc;

[0034] The center of the third sector-shaped metal disc is connected to the connection between the first microstrip line and the second microstrip line; the center of the first symmetric sector-shaped metal disc is connected to the connection between the third microstrip line and the fourth microstrip line; the center of the second symmetric sector-shaped metal disc is connected to the connection between the seventh microstrip line and the eighth microstrip line; the center of the third sector-shaped metal disc is connected to the connection between the eighth microstrip line and the ninth microstrip line.

[0035] In summary, due to the adoption of the above technical solutions, the beneficial effects of the present invention are:

[0036] 1. The present invention uses a generalized pole extraction synthesis method to construct transmission zeros to realize complex functions, enabling the filter design to have a relative bandwidth of 40% while having high selectivity.

[0037] 2. The topology in the prototype circuit can be transformed into a similar circuit structure design, facilitating unified transformation of the circuit similar structure when replacing lumped parameter elements, and greatly simplifying the design process and steps.

[0038] 3. Circuit transformation is performed on the lumped element circuit synthesized based on the generalized pole extraction synthesis method, avoiding the problem of parasitic parameter interference of lumped parameter elements at high frequencies during the filter design process. While maintaining the zeros, it is converted into a distributed circuit, and at the same time has a wide bandwidth.

[0039] 4. The converted distributed parameter element circuit uses the method of impedance transformation to normalize the characteristic impedance of different transmission lines to a smaller value, making it convenient to be realized by microstrip technology, reducing production costs, improving manufacturing efficiency, and at the same time avoiding the problem of stepped impedance transitional connection, greatly improving the stability of the filter operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] The present invention will be described by way of examples with reference to the accompanying drawings, wherein:

[0041] Figure 1 is an embodiment of the prototype circuit of the broadband microwave filter of the present invention.

[0042] Figure 2 is a schematic diagram of replacing lumped parameter elements with distributed parameter elements in the present invention.

[0043] Figure 3 is a schematic diagram of the impedance transformation process in the present invention.

[0044] Figure 4 is an embodiment of the broadband microwave filter of the present invention.

[0045] Figure 5 is the overall response diagram of the broadband microwave filter of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0046] All features disclosed in this specification, or all steps in the disclosed methods or processes, except for mutually exclusive features and / or steps, can be combined in any way.

[0047] Any feature disclosed in this specification (including any additional claims, abstract) can be replaced by other equivalent or similar-purpose alternative features unless specifically stated otherwise. That is, unless specifically stated otherwise, each feature is only an example of a series of equivalent or similar features.

[0048] Embodiment 1

[0049] A method for implementing a broadband microwave filter, the method comprising the following steps:

[0050] S1. Construct a transfer zero point through a generalized pole extraction synthesis method to realize a complex function, and obtain a prototype circuit of a broadband microwave filter with multiple transfer zero points constructed by lumped parameter elements, so that the broadband microwave filter design has a relative bandwidth of 40% and high selectivity at the same time.

[0051] The generalized pole extraction synthesis method belongs to a conventional method, which is a method for obtaining a prototype circuit of a filter according to a prototype function of the filter. First, calculate the ABCD matrix of the overall circuit network according to the prototype function polynomial FPE, and then split the ABCD matrix of each component module one by one from the overall network according to the circuit components to be extracted until the extraction is completed. In the embodiment of the present invention, the generalized pole extraction synthesis method can extract a pole unit circuit corresponding to the transfer zero point in the filter function. The extraction process according to the topological structure of the circuit includes: obtaining the FPE polynomial according to the filter index and obtaining the ABCD matrix of the overall circuit. The extraction process includes: 1) extracting a series inductor, 2) extracting a series reactance, 3) extracting a parallel pole, and 4) extracting a parallel susceptance. And so on until the last series inductor is extracted.

[0052] The transfer zero point in the broadband microwave filter introduces multiple transfer zero points by connecting multiple resonator stubs in parallel. Taking the design of 3 transfer zero points as an example, in the prototype circuit (main path) of the broadband microwave filter, 3 series LC resonators are connected in parallel. See the appendix for the prototype circuit Figure 1 as shown, corresponding to Figure 4 in the distributed parameter element circuit topological structure, 3 series LC resonators are converted into 3 resonator branches.

[0053] In addition, when solving the prototype circuit, it is preferably to transform the topological structure of the prototype circuit into a similar circuit structure, that is, to use as many lumped parameter elements of one module as possible. As Figure 1 shown, the prototype circuit with 3 transfer zero points is transformed into a topological structure mainly constructed by series LC resonators, Figure 1 which contains 7 series LC resonators and has a medium bandwidth with an operating frequency of 4 - 8 GHz. In this way, when replacing with distributed parameter elements later, unified replacement can be carried out, which is convenient and fast.

[0054] S2. Transform the lumped parameter element circuit topological structure of the prototype circuit into a distributed parameter element circuit topological structure, that is, replace the lumped parameter elements in the prototype circuit with distributed parameter elements.

[0055] As Figure 2As shown, in some embodiments, a half-wavelength resonator is used to replace the series LC resonator; a high-impedance transmission line is used to replace the inductive element; a sector-shaped metal sheet is used to replace the grounded capacitor and the susceptance element that does not change with frequency.

[0056] The parallel resonator stubs can arbitrarily control the transmission zeros. According to the frequencies at which the zeros are generated, the parallel resonator stubs adopt different implementation forms. In the resonator stubs introducing high-end transmission zeros, the series LC resonator is implemented by an open-circuit quarter-wavelength resonator; in the resonator stubs introducing low-end transmission zeros, the inductor is implemented by a high-impedance transmission line, and the capacitor is implemented by a sector-shaped metal sheet.

[0057] S3. Perform impedance transformation on the distributed element circuit topology to reduce the characteristic impedance of the transmission line.

[0058] For the impedance transformation process, first, the high-impedance transmission line in the distributed element circuit topology is converted into a low-impedance transmission line, and then the lumped parameter elements in the converted circuit topology are replaced with distributed parameter elements.

[0059] In some embodiments, a section of high-impedance transmission line is converted into more than one section of low-impedance transmission line, and susceptance elements that do not change with frequency are respectively introduced at both ends of the multiple sections of low-impedance transmission line and between adjacent low-impedance transmission lines. Taking the conversion of a section of high-impedance transmission line into two sections of low-impedance transmission line as an example, a section of high-impedance transmission line is converted into two sections of low-impedance transmission line, and susceptance elements that do not change with frequency are respectively introduced at both ends of the multiple sections of low-impedance transmission line and between the two sections of low-impedance transmission line.

[0060] The multiple sections of low-impedance transmission line usually have the same structure, that is, the same parameters. For example, a section of high-impedance transmission line is converted into two sections of low-impedance transmission line with the same parameters. The process is as Figure 3 shown. The high-impedance transmission line is converted into two transition transmission lines with equal characteristic admittance and length. Assume that the characteristic admittance of the high-impedance transmission line is Y0 and the length is θ0, and it is converted into two transition transmission lines with a length of θ1 and a characteristic admittance of Y0; then the two transition transmission lines are converted into two low-impedance transmission lines with a characteristic admittance of Y1 and a length of θ2. In addition, susceptance elements B1 and B3 that do not change with frequency are respectively introduced at both ends of the two low-impedance transmission lines, B1 and B3 are exactly the same, and a susceptance element B2 (the values are also represented by B1, B2, and B3 respectively) is introduced in the middle.

[0061] Specifically, the relationships among the high-impedance transmission line, the transition transmission line, the low-impedance transmission line, and the three susceptance elements are:

[0062] Y1 = kY0cscθ2 / cscθ1

[0063] B1 = Y1 cotθ2 - Y0 cotθ1

[0064] B2 = 2Y1 cotθ2 - 2k 2 Y0 cotθ1

[0065] B3 = Y1 cotθ2 - Y0 cotθ1.

[0066] Preferably, a low - impedance transmission line with a characteristic impedance of 80 ohms and a line width of 0.1 mm is convenient to be processed and realized by the microstrip process.

[0067] Embodiment 2

[0068] This embodiment discloses a broadband microwave filter, which is designed by using the design method of Embodiment 1.

[0069] This embodiment takes the design of a medium - broadband microwave filter with 3 transmission zeros as an example for illustration. The 7 - order band - pass microwave filter with 3 transmission zeros operates in the range of 4 - 8 GHz. As Figure 1 shown, the main path (between the input Input and output Output ports) of the bandwidth microwave filter includes 4 series - connected series LC resonators, 3 LC resonator stubs, and 3 parallel susceptance elements B4, B5, B6 that do not change with frequency. The 3 LC resonator stubs are respectively connected between every two adjacent series LC resonators, and the 3 susceptance elements are respectively connected between every two adjacent series LC resonators. The 3 series - connected LC resonators are respectively the first LC resonator formed by the series connection of inductor L1 and capacitor C1, the second LC resonator formed by the series connection of inductor L2 and capacitor C2, the third LC resonator formed by the series connection of inductor L3 and capacitor C3, and the fourth LC resonator formed by the series connection of inductor L4 and capacitor C4. The 3 LC resonator stubs are respectively the first LC resonator stub formed by the series connection of inductor L z1 and capacitor C z1 series, the second LC resonator stub formed by the series connection of inductor L z2 and capacitor C z2 series, the third LC resonator stub formed by the series connection of inductor L z3 and capacitor C z3 series.

[0070] As Figure 4 shown, the first port Port 1 of the bandwidth microwave filter is sequentially connected to the first microstrip line section M1, the second microstrip line section M2, the third microstrip line section M3, the fourth microstrip line section M4, the fifth microstrip line section M5, the sixth microstrip line section M6, the seventh microstrip line section M7, the eighth microstrip line section M8, the ninth microstrip line section M9, the tenth microstrip line section M10 and the second port Port 2 along the main path;

[0071] The upper end of the eleventh microstrip line section M11 connected to the branch is connected to the connection point of the first microstrip line M1 and the second microstrip line M2, and the lower end is connected to the first sector-shaped metal disc C2; the upper end of the twelfth microstrip line section M12 connected to the branch is connected to the connection point of the second microstrip line M2 and the third microstrip line M3; the upper end of the thirteenth microstrip line section M13 connected to the branch is connected to the connection point of the fourth microstrip line M4 and the fifth microstrip line M5; the upper end of the fourteenth microstrip line section M14 connected to the branch is connected to the connection point of the fifth microstrip line M5 and the sixth microstrip line M6; the lower end of the fifteenth microstrip line section M15 connected to the branch is connected to the connection point of the fifth microstrip line M5 and the sixth microstrip line M6; the lower end of the sixteenth microstrip line section M16 connected to the branch is connected to the connection point of the sixth microstrip line M6 and the seventh microstrip line M7; the lower end of the seventeenth microstrip line section M17 connected to the branch is connected to the connection point of the eighth microstrip line M8 and the ninth microstrip line M9; the upper end of the eighteenth microstrip line section M18 connected to the branch is connected to the connection point of the ninth microstrip line M9 and the tenth microstrip line M10, and the lower end is connected to the second sector-shaped metal disc C6;

[0072] The center of the third sector-shaped metal disc C1 is connected to the connection point of the first microstrip line M1 and the second microstrip line M2; the center of the first symmetric sector-shaped metal disc C3 is connected to the connection point of the third microstrip line M3 and the fourth microstrip line M4; the center of the second symmetric sector-shaped metal disc C4 is connected to the connection point of the seventh microstrip line M7 and the eighth microstrip line M8; the center of the third sector-shaped metal disc C5 is connected to the connection point of the eighth microstrip line M8 and the ninth microstrip line M9.

[0073] Same as Embodiment 1, preferably all microstrip line sections are 80 ohms, and the corresponding line width is 0.1 mm.

[0074] The broadband microwave filter of this embodiment is tested, and the response diagram as Figure 5 shown is obtained. It can be seen from Figure 5 this that the broadband microwave filter provided by this embodiment has a relative bandwidth of 40%, low insertion loss, two transmission zeros at the low end of the passband, and one transmission zero at the high end of the passband, and has high selectivity.

[0075] The present invention is not limited to the foregoing specific embodiments. The present invention extends to any new feature or any new combination disclosed in this specification, as well as any new method or process step or any new combination disclosed.

Claims

1. A method for implementing a broadband microwave filter, characterized in that, Including: Construct a complex function by constructing transmission zeros through a generalized pole extraction synthesis method, and obtain a prototype circuit of a broadband microwave filter with multiple transmission zeros constructed by lumped parameter elements; Transform the circuit topology of the lumped parameter elements of the prototype circuit into a circuit topology of distributed parameter elements; Perform impedance transformation on the circuit topology of the distributed elements to reduce the characteristic impedance of the transmission line.

2. The implementation method of the broadband microwave filter according to claim 1, characterized in that, In the circuit topology of the distributed parameter elements of the broadband microwave filter, introduce multiple transmission zeros by connecting multiple resonator stubs in parallel.

3. The implementation method of the broadband microwave filter according to claim 2, wherein Among the multiple resonator stubs connected in parallel, in the resonator stub introducing the high-end transmission zero, the series LC resonator is realized by an open-circuit quarter-wavelength resonator; in the resonator stub introducing the low-end transmission zero, the inductor is realized by a high-impedance transmission line, and the capacitor is realized by a fan-shaped metal sheet.

4. The implementation method of the broadband microwave filter according to claim 1, characterized in that Transforming the circuit topology of the lumped parameter elements of the prototype circuit into a circuit topology of distributed parameter elements includes: Replacing the series LC resonator with a half-wavelength resonator; replacing the inductor element with a high-impedance transmission line; replacing the grounded capacitor and the susceptance element that does not change with frequency with a fan-shaped metal sheet.

5. The implementation method of the broadband microwave filter according to claim 1, characterized in that, The impedance transformation of the circuit topology of the distributed parameter elements includes: Converting the high-impedance transmission line in the circuit topology of the distributed elements into a low-impedance transmission line; Replacing the lumped parameter elements in the transformed circuit topology with distributed parameter elements.

6. The implementation method of the broadband microwave filter according to claim 5, characterized in that, The conversion of the high-impedance transmission line in the circuit topology of the distributed elements into a low-impedance transmission line includes: Converting at least one section of the high-impedance transmission line in the circuit topology of the distributed elements into two sections of low-impedance transmission lines, and introducing susceptance elements that do not change with frequency at both ends and in the middle of the two sections of low-impedance transmission lines.

7. The implementation method of the broadband microwave filter according to claim 6, characterized in that, The process of converting the high-impedance transmission line into two sections of low-impedance transmission lines and introducing susceptance elements that do not change with frequency at both ends and in the middle of the two sections of low-impedance transmission lines includes: Converting the high-impedance transmission line into two transition transmission lines with equal characteristic admittance and length; Converting the two transition transmission lines into two sections of low-impedance transmission lines with equal characteristic admittance and length, and introducing susceptance elements that do not change with frequency at both ends and in the middle of the two sections of low-impedance transmission lines, and the susceptance elements at both ends are the same.

8. The implementation method of the broadband microwave filter according to claim 7, characterized in that, The relationship among the high-impedance transmission line, the transition transmission line, the low-impedance transmission line, and the three susceptance elements is: Y1 = kY0cscθ2 / cscθ1 B1 = Y1cotθ2 - Y0cotθ1 B2 = 2Y1cotθ2 - 2k 2 Y0cotθ1 B3 = Y1cotθ2 - Y0cotθ1 Wherein, Y0 and Y1 are the characteristic admittances of the high-impedance transmission line and the low-impedance transmission line respectively, θ0, θ1, and θ2 are the transmission line lengths of the high-impedance transmission line, the transition transmission line, and the low-impedance transmission line respectively, B1 and B3 are the values of the susceptance elements at both ends, B2 is the value of the susceptance element in the middle, and k is the conversion coefficient.

9. A medium-bandwidth microwave filter designed by the implementation method of the broadband microwave filter according to any one of claims 1 to 8, characterized in that, The main path of the medium-bandwidth microwave filter includes four series-connected LC resonators, three LC resonator stubs, and three shunt susceptance elements that do not vary with frequency; the three LC resonator stubs are respectively connected between every two adjacent series LC resonators, and the three susceptance elements are respectively connected between every two adjacent series LC resonators.

10. The medium bandwidth microwave filter according to claim 9, characterized in that, The first port (Port 1) of the medium-bandwidth microwave filter is sequentially connected along the main path to the first microstrip line section (M1), the second microstrip line section (M2), the third microstrip line section (M3), the fourth microstrip line section (M4), the fifth microstrip line section (M5), the sixth microstrip line section (M6), the seventh microstrip line section (M7), the eighth microstrip line section (M8), the ninth microstrip line section (M9), the tenth microstrip line section (M10), and the second port (Port 2); The upper end of the eleventh microstrip line section (M11) connected to the branch is connected to the connection between the first microstrip line (M1) and the second microstrip line (M2), and the lower end is connected to the first sector-shaped metal disc (C2); the upper end of the twelfth microstrip line section (M12) connected to the branch is connected to the connection between the second microstrip line (M2) and the third microstrip line (M3); the upper end of the thirteenth microstrip line section (M13) connected to the branch is connected to the connection between the fourth microstrip line (M4) and the fifth microstrip line (M5); the upper end of the fourteenth microstrip line section (M14) connected to the branch is connected to the connection between the fifth microstrip line (M5) and the sixth microstrip line (M6); the lower end of the fifteenth microstrip line section (M15) connected to the branch is connected to the connection between the fifth microstrip line (M5) and the sixth microstrip line (M6); the lower end of the sixteenth microstrip line section (M16) connected to the branch is connected to the connection between the sixth microstrip line (M6) and the seventh microstrip line (M7); the lower end of the seventeenth microstrip line section (M17) connected to the branch is connected to the connection between the eighth microstrip line (M8) and the ninth microstrip line (M9); the upper end of the eighteenth microstrip line section (M18) connected to the branch is connected to the connection between the ninth microstrip line (M9) and the tenth microstrip line (M10), and the lower end is connected to the second sector-shaped metal disc (C6); The center of the third sector-shaped metal disc (C1) is connected to the connection between the first microstrip line (M1) and the second microstrip line (M2); the center of the first symmetric sector-shaped metal disc (C3) is connected to the connection between the third microstrip line (M3) and the fourth microstrip line (M4); the center of the second symmetric sector-shaped metal disc (C4) is connected to the connection between the seventh microstrip line (M7) and the eighth microstrip line (M8); The center of the third sector-shaped metal disc (C5) is connected to the connection between the eighth microstrip line (M8) and the ninth microstrip line (M9).

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