Microstrip band-pass filter topological structure and filter
By designing a microstrip bandpass filter topology structure including input end, parallel three lines, parallel lines and short-circuit branches, the existing microstrip bandpass filter structure is solved, and the passband is realized Microband filter with flatness and high selectivity of stopband, suitable for modern wireless communication systems.
Patent Information
- Application Number
- CN202421049833.2
- Authority / Receiving Office
- CN · China
- Patent Type
- Utility models(China)
- Current Assignee / Owner
- Filing Date
- 2024-05-13
- Publication Date
- 2025-01-17
- Estimated Expiration
- 2034-05-13
AI Technical Summary
The existing microstrip bandpass filters are not compact in structure and have low selectivity, limiting their application in modern wireless communication systems.
A microstrip bandpass filter topology structure including input end, parallel three lines, parallel lines and short-circuit branches is designed. Through the arrangement and characteristic impedance settings of microstrip lines and short-circuit branches, the filter has high selectivity and Miniaturization features.
The topological design of the microstrip bandpass filter has six transmission poles and four transmission zeros, ensuring the flatness of the passband and the high selectivity and isolation of the stopband, achieving the miniaturization and selection of the filter Advantages of high sensitivity.
Smart Images
Figure CN222365713U_ABST
Abstract
Description
Technical Field
[0001] The utility model relates to the technical field of filters, in particular to a microstrip bandpass filter topology structure and a filter. Background Art
[0002] Wideband bandpass filters based on microstrip structures have attracted extensive attention and in-depth research from scholars and engineers in the industry due to their advantages of low profile, small size, light weight, simple design, high-speed data transmission, and easy integration with other components. However, the wideband bandpass filters based on microstrip structures that have been reported so far often have problems such as non-compact structure and low selectivity, which are not conducive to system miniaturization and efficient use of spectrum, and greatly limit their use in modern wireless communication systems. Utility Model Content
[0003] The main purpose of the utility model is to provide a microstrip bandpass filter topology structure and a filter, aiming to solve the problems of the existing microstrip bandpass filter having a non-compact structure and low selectivity.
[0004] To achieve the above object, the utility model proposes a microstrip bandpass filter topology structure, comprising an input end, a first parallel three wires, a first parallel wire, a second parallel three wires and an output end connected in sequence;
[0005] One end of the first parallel three lines connected to the first parallel line is symmetrically connected to a first microstrip line and a second microstrip line, the other end of the first microstrip line is connected to a first short-circuit branch, and the other end of the second microstrip line is connected to a second short-circuit branch;
[0006] The third microstrip line and the fourth microstrip line are symmetrically connected to one end of the second parallel three-line connected to the first parallel line, the third microstrip line is connected to a third short-circuit branch at the other end, and the fourth microstrip line is connected to a fourth short-circuit branch at the other end;
[0007] The first parallel line, the first three parallel lines, the second three parallel lines, the first short-circuit branch, the second short-circuit branch, the third short-circuit branch and the fourth short-circuit branch are all arranged along the first direction, the first microstrip line, the second microstrip line, the third microstrip line and the fourth microstrip line are all arranged along the second direction, and the first direction is perpendicular to the second direction.
[0008] Optionally, the odd-mode characteristic impedance of the first three parallel lines is equal to the odd-mode characteristic impedance of the second three parallel lines, and the even-mode characteristic impedance of the first three parallel lines is equal to the even-mode characteristic impedance of the second three parallel lines.
[0009] Optionally, the characteristic impedance of the first microstrip line, the characteristic impedance of the second microstrip line, the characteristic impedance of the third microstrip line, the characteristic impedance of the fourth microstrip line, the characteristic impedance of the first short-circuit branch, the characteristic impedance of the second short-circuit branch, the characteristic impedance of the third short-circuit branch and the characteristic impedance of the fourth short-circuit branch are equal.
[0010] Optionally, the electrical length of the first parallel line, the electrical length of the first three parallel lines, and the electrical length of the second three parallel lines are equal, and are all equal to a quarter wavelength corresponding to the center frequency of the broadband bandpass filter.
[0011] Optionally, the electrical length of the first microstrip line is equal to the electrical length of the fourth microstrip line; the electrical length of the second microstrip line is equal to the electrical length of the third microstrip line.
[0012] Optionally, the electrical length of the first short-circuit branch is equal to the electrical length of the fourth short-circuit branch; the electrical length of the second short-circuit branch is equal to the electrical length of the third short-circuit branch.
[0013] Optionally, the sum of the electrical length of the first microstrip line and the electrical length of the first short-circuit branch, the sum of the electrical length of the second microstrip line and the electrical length of the second short-circuit branch, the sum of the electrical length of the third microstrip line and the electrical length of the third short-circuit branch, and the sum of the electrical length of the fourth microstrip line and the electrical length of the fourth short-circuit branch are equal, and are all greater than one-quarter wavelength corresponding to the center frequency of the broadband bandpass filter.
[0014] To achieve the above object, the utility model further proposes a filter, comprising any of the above-mentioned microstrip bandpass filter topology structures.
[0015] Optionally, the filter further includes a circuit board, and the topological structure is integrated on the circuit board.
[0016] Optionally, the lengths of the first three parallel lines and the second three parallel lines are equal, and are set to be l T ; The spacing between the transmission lines constituting the first parallel three lines or the second parallel three lines is equal, set to s T The width of the transmission lines constituting the first three parallel lines or the second three parallel lines is equal, set to w T ;
[0017] The length of the first parallel line is set to l p ; The spacing between the transmission lines constituting the first parallel line is set to s p The width of the transmission line constituting the first parallel line is set to w p ;
[0018] The lengths of the first microstrip line and the fourth microstrip line are equal, set to l1; the lengths of the first short-circuit branch and the fourth short-circuit branch are equal, set to l2; the lengths of the second microstrip line and the third microstrip line are equal, set to l3; the lengths of the second short-circuit branch and the third short-circuit branch are equal, set to l4;
[0019] The width of the first microstrip line, the width of the second microstrip line, the width of the third microstrip line, the width of the fourth microstrip line, the width of the first short-circuit branch, the width of the second short-circuit branch, the width of the third short-circuit branch and the width of the fourth short-circuit branch are equal and set to w1.
[0020] The beneficial effect of the utility model is that the topological structure of the existing bandpass filter is improved, and the bandpass filter designed based on the topological structure is a microstrip bandpass filter. There are six transmission poles in the passband to ensure the flatness of the passband, and there are four transmission zeros in the stopband to ensure the high selectivity and high isolation of the filter. The microstrip bandpass filter based on the topological structure has the advantages of miniaturization and high selectivity. BRIEF DESCRIPTION OF THE DRAWINGS
[0021] In order to more clearly illustrate the embodiments of the utility model or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the utility model. For ordinary technicians in this field, other drawings can be obtained based on the structures shown in these drawings without paying creative work.
[0022] Figure 1 This is a schematic diagram of the topological structure of the filter of the utility model;
[0023] Figure 2 It is an odd-mode diagram of the topological structure of the utility model;
[0024] Figure 3 It is an even-mode diagram of the topological structure of the utility model;
[0025] Figure 4 This is a layout diagram of the filter of the utility model;
[0026] Figure 5 This is a diagram of the S parameter simulation results of the utility model filter;
[0027] The realization of the purpose, functional features and advantages of the utility model will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION
[0028] The following will be combined with the drawings in the embodiments of the utility model to clearly and completely describe the technical solutions in the embodiments of the utility model. Obviously, the described embodiments are only part of the embodiments of the utility model, not all of the embodiments. Based on the embodiments of the utility model, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the utility model.
[0029] It should be noted that if the embodiments of the present invention involve directional indications (such as up, down, left, right, front, back...), the directional indications are only used to explain the relative position relationship, movement status, etc. between the components under a certain specific posture (as shown in the accompanying drawings). If the specific posture changes, the directional indication will also change accordingly.
[0030] In addition, if there are descriptions involving "first", "second", etc. in the embodiments of the utility model, the descriptions of "first", "second", etc. are only used for descriptive purposes and cannot be understood as indicating or implying their relative importance or implicitly indicating the number of technical features indicated. Therefore, the features defined as "first" and "second" may explicitly or implicitly include at least one of the features. In addition, if the meaning of "and / or" appearing in the full text is to include three parallel schemes, taking "A and / or B" as an example, it includes scheme A, or scheme B, or a scheme that satisfies both A and B. In addition, the technical solutions between the various embodiments can be combined with each other, but it must be based on the ability of ordinary technicians in this field to implement. When the combination of technical solutions is contradictory or cannot be implemented, it should be deemed that such a combination of technical solutions does not exist and is not within the scope of protection required by the utility model.
[0031] An embodiment of the present invention provides a microstrip bandpass filter topology structure, referring to Figure 1 , including an input terminal, a first parallel three wires, a first parallel wire, a second parallel three wires and an output terminal connected in sequence;
[0032] One end of the first parallel three lines connected to the first parallel line is symmetrically connected to a first microstrip line and a second microstrip line, the other end of the first microstrip line is connected to a first short-circuit branch, and the other end of the second microstrip line is connected to a second short-circuit branch;
[0033] The third microstrip line and the fourth microstrip line are symmetrically connected to one end of the second parallel three-line connected to the first parallel line, the third microstrip line is connected to a third short-circuit branch at the other end, and the fourth microstrip line is connected to a fourth short-circuit branch at the other end;
[0034] The first parallel line, the first three parallel lines, the second three parallel lines, the first short-circuit branch, the second short-circuit branch, the third short-circuit branch and the fourth short-circuit branch are all arranged along the first direction, the first microstrip line, the second microstrip line, the third microstrip line and the fourth microstrip line are all arranged along the second direction, and the first direction is perpendicular to the second direction.
[0035] This embodiment improves the topological structure of the existing bandpass filter, which is composed of a parallel line, a pair of parallel three lines, four microstrip lines and four short-circuit branches. Among them, the first parallel three lines and the second parallel three lines are symmetrical about the first parallel line. The first microstrip line and the second microstrip line, the first short-circuit branch and the second short-circuit branch are symmetrical about the first parallel three lines, respectively, and the third microstrip line and the fourth microstrip line, the third short-circuit branch and the fourth short-circuit branch are symmetrical about the second parallel three lines; the first microstrip line and the third microstrip line, the second microstrip line and the fourth microstrip line, the first short-circuit branch and the third short-circuit branch, the second short-circuit branch and the fourth short-circuit branch are symmetrical about the first parallel line.
[0036] Furthermore, the first parallel three lines and the second parallel three lines are respectively composed of three parallel and equidistant transmission lines, wherein the two outermost transmission lines of the first parallel three lines are used to connect the input end, and the transmission line in the middle of the first parallel three lines is used to connect the first microstrip line and the second microstrip line; the two outermost transmission lines of the second parallel three lines are used to connect the output end, and the transmission line in the middle of the second parallel three lines is used to connect the third microstrip line and the fourth microstrip line; the first parallel lines are composed of two parallel transmission lines.
[0037] Furthermore, the odd-mode characteristic impedance of the first three parallel lines is equal to the odd-mode characteristic impedance of the second three parallel lines, and the even-mode characteristic impedance of the first three parallel lines is equal to the even-mode characteristic impedance of the second three parallel lines. In this embodiment, the odd-mode characteristic impedance of the first three parallel lines and the odd-mode characteristic impedance of the second three parallel lines are set to Z o1 , the even-mode characteristic impedance of the first three parallel lines and the even-mode characteristic impedance Z of the second three parallel lines e1 The odd-mode characteristic impedance of the first parallel line is set to Z o2 ; The even-mode characteristic impedance of the first parallel line is set to Z e2 .
[0038] The characteristic impedance of the first microstrip line, the characteristic impedance of the second microstrip line, the characteristic impedance of the third microstrip line, the characteristic impedance of the fourth microstrip line, the characteristic impedance of the first short-circuit branch, the characteristic impedance of the second short-circuit branch, the characteristic impedance of the third short-circuit branch, and the characteristic impedance of the fourth short-circuit branch are equal. In this embodiment, the characteristic impedance of the first microstrip line, the characteristic impedance of the second microstrip line, the characteristic impedance of the third microstrip line, the characteristic impedance of the fourth microstrip line, the characteristic impedance of the first short-circuit branch, the characteristic impedance of the second short-circuit branch, the characteristic impedance of the third short-circuit branch, and the characteristic impedance of the fourth short-circuit branch are all set to Z1.
[0039] Further, the electrical length of the first parallel line, the electrical length of the first three parallel lines, and the electrical length of the second three parallel lines are equal, and are all equal to a quarter wavelength corresponding to the center frequency of the broadband bandpass filter;
[0040] The electrical length of the first microstrip line is equal to the electrical length of the fourth microstrip line; the electrical length of the second microstrip line is equal to the electrical length of the third microstrip line;
[0041] The electrical length of the first short-circuit branch is equal to the electrical length of the fourth short-circuit branch; the electrical length of the second short-circuit branch is equal to the electrical length of the third short-circuit branch;
[0042] The sum of the electrical length of the first microstrip line and the electrical length of the first short-circuit branch, the sum of the electrical length of the second microstrip line and the electrical length of the second short-circuit branch, the sum of the electrical length of the third microstrip line and the electrical length of the third short-circuit branch, and the sum of the electrical length of the fourth microstrip line and the electrical length of the fourth short-circuit branch are equal, and are all greater than one-quarter wavelength corresponding to the center frequency of the broadband bandpass filter.
[0043] Since the topology is a symmetrical structure, its transmission poles can be calculated using the odd-even mode method. To simplify the calculation process, it is first assumed that the sum of the electrical length of the first microstrip line and the electrical length of the first short-circuit branch is equal to a quarter wavelength corresponding to the center frequency of the broadband bandpass filter. At this time, Figure 2 It is an odd-mode diagram of the simplified topological structure. Among them, the electrical length of the odd-mode transmission line is the electrical length of the first three parallel lines; the characteristic impedance of the odd-mode transmission line is the odd-mode characteristic impedance of the first three parallel lines.
[0044] refer to Figure 2 , when Y ino = 0, it can be concluded that the topology has four transmission poles. When f0 is the center frequency of the bandpass filter, the frequencies corresponding to the four odd-mode transmission poles are:
[0045]
[0046]
[0047]
[0048]
[0049] in,
[0050] Δ o1 =2Z1(Z e1 -Z o1 ) 2
[0051] Δ o2 =4Z1Z o2 (Z e1 +Z o1 )+8Z1Z o1 Z e1 +Z o2 (Z e1 -Z o1 ) 2
[0052] Δ o3 =4Z o1 Z e1 Z o2
[0053] Figure 3 is the even-mode form diagram of the simplified topological structure. Among them, the electrical length of the even-mode transmission line is the electrical length of the first three parallel lines; the characteristic impedance of the even-even-mode transmission line is the even-mode characteristic impedance of the first three parallel lines. ino = 0, it can be concluded that the topology has four transmission poles. When f0 is the center frequency of the bandpass filter, the frequencies corresponding to the four even-mode transmission poles are:
[0054]
[0055]
[0056]
[0057]
[0058] in,
[0059] Δ1=2Z e1 (Z e1 -Z o1 ) 2
[0060] Δ e2 =4Z1Z e2 (Z e1 +Z o1 )+8Z1Z o1 Ze1 +Z e2 (Z e1 -Z o1 ) 2
[0061] Δ e3 =4Z o1 Z e1 Z e2
[0062] For this topology, its transmission zero point can be calculated by the following method: multiply the ABCD matrices of the cascaded resonators that make up the topology in sequence to obtain the ABCD matrix corresponding to the topology; and convert the ABCD matrix of the topology into the corresponding S matrix. 21 When |=0, it can be concluded that this topology has two transmission zeros, and the frequencies corresponding to the two transmission zeros are:
[0063] f z1 =0
[0064] f z2 =2f0
[0065] From the above analysis, it can be seen that when the sum of the electrical length of the first microstrip line and the electrical length of the first short-circuit branch is equal to a quarter wavelength corresponding to the center frequency of the broadband bandpass filter, the topology has four odd-mode transmission poles, four even-mode transmission poles and two transmission zeros. Returning to this topology, when the sum of the electrical length of the first microstrip line and the electrical length of the first short-circuit branch is appropriately increased, two additional transmission zeros (f z3 , f z4 ), but the number of original zeros and poles remains unchanged. And no matter how the parameter Z is changed o1 , Z e1 , Z o2 , Z e2 , the value of Z1, the relative position of the transmission zero pole, that is, f z1 <f z3 <f ep1 <f op1 <f op2 <f ep2 <f ep3 <f op3 <f op4 <f ep4 <f z4 <f z2 , will not change. Therefore, based on this topology, a broadband bandpass filter can be designed with eight transmission poles in the passband to ensure its in-band flatness and four transmission zeros in the stopband to ensure high selectivity and high isolation.
[0066] An embodiment of the present invention provides a filter, comprising any of the above-mentioned microstrip bandpass filter topology structures.
[0067] Furthermore, the filter also includes a circuit board, and the topological structure is integrated on the circuit board.
[0068] The lengths of the first three parallel lines and the second three parallel lines are equal and are set to l T ; The spacing between the transmission lines constituting the first parallel three lines or the second parallel three lines is equal, set to s T The width of the transmission lines constituting the first three parallel lines or the second three parallel lines is equal, set to w T ;
[0069] The length of the first parallel line is set to l p ; The spacing between the transmission lines constituting the first parallel line is set to s p The width of the transmission line constituting the first parallel line is set to w p ;
[0070] The lengths of the first microstrip line and the fourth microstrip line are equal, set to l1; the lengths of the first short-circuit branch and the fourth short-circuit branch are equal, set to l2; the lengths of the second microstrip line and the third microstrip line are equal, set to l3; the lengths of the second short-circuit branch and the third short-circuit branch are equal, set to l4;
[0071] The width of the first microstrip line, the width of the second microstrip line, the width of the third microstrip line, the width of the fourth microstrip line, the width of the first short-circuit branch, the width of the second short-circuit branch, the width of the third short-circuit branch and the width of the fourth short-circuit branch are equal and set to w1.
[0072] In this embodiment, in order to verify the characteristics of the above topological structure, a microstrip bandpass filter is designed based on the above topological structure. The filter is designed on a circuit board with a dielectric constant of 3.38, a dielectric loss of 0.0022, and a thickness of 0.813 mm, and the size of the circuit board is 34.4 mm*13.3 mm.
[0073] refer to Figure 4 , the lengths of the first three parallel lines and the second three parallel lines are equal, set to l T =9.8mm; the spacing between the transmission lines constituting the first parallel three lines or the second parallel three lines is equal, set to s T =0.1mm; the width of the transmission lines constituting the first three parallel lines or the second three parallel lines is equal, set to w T =0.2mm;
[0074] The length of the first parallel line is set to l p=9.8mm; the spacing between the transmission lines constituting the first parallel line is set to s p =0.1mm; the width of the transmission line constituting the first parallel line is set to w p =0.2mm;
[0075] The lengths of the first microstrip line and the fourth microstrip line are equal, and are set to l1=5.9 mm; the lengths of the first short-circuit branch and the fourth short-circuit branch are equal, and are set to l2=4.8 mm; the lengths of the second microstrip line and the third microstrip line are equal, and are set to l3=6.2 mm; the lengths of the second short-circuit branch and the third short-circuit branch are equal, and are set to l4=4.5 mm;
[0076] The width of the first microstrip line, the width of the second microstrip line, the width of the third microstrip line, the width of the fourth microstrip line, the width of the first short-circuit branch, the width of the second short-circuit branch, the width of the third short-circuit branch and the width of the fourth short-circuit branch are equal and are set to w1=0.7mm.
[0077] Based on the filter designed based on the above topology, S parameter simulation is performed, and the simulation results are referenced Figure 5 It can be seen that the passband range with a reflection coefficient better than -10dB is 2.265GHz to 7.229GHz, the center frequency is 4.747GHz, the absolute bandwidth is 4.964GHz, and the relative bandwidth is 104.6%. In addition, there are six transmission poles in the passband, located at 2.341, 2.518, 3.423, 3.985, 5.484, 6.703, GHz, respectively. These six transmission poles ensure the flatness of the passband. There are four transmission zeros in the stopband, located at 0, 1.305, 7.578, 10.359GHz, respectively. These four transmission zeros ensure the high selectivity and high isolation of the filter.
[0078] Therefore, the topological structure of this embodiment can be used to design a microstrip bandpass filter, and the filter has the advantages of miniaturization and high selectivity.
[0079] The above description is only an optional embodiment of the utility model, and does not limit the patent scope of the utility model. All equivalent structural changes made by using the contents of the utility model specification and drawings under the utility model concept, or directly / indirectly used in other related technical fields are included in the patent protection scope of the utility model.
Claims
1. A microstrip bandpass filter topology structure, characterized in that: It includes an input terminal, a first parallel three wires, a first parallel wire, a second parallel three wires and an output terminal connected in sequence; One end of the first parallel three lines connected to the first parallel line is symmetrically connected to a first microstrip line and a second microstrip line, the other end of the first microstrip line is connected to a first short-circuit branch, and the other end of the second microstrip line is connected to a second short-circuit branch; The third microstrip line and the fourth microstrip line are symmetrically connected to one end of the second parallel three-line connected to the first parallel line, the third microstrip line is connected to a third short-circuit branch at the other end, and the fourth microstrip line is connected to a fourth short-circuit branch at the other end; The first parallel line, the first three parallel lines, the second three parallel lines, the first short-circuit branch, the second short-circuit branch, the third short-circuit branch and the fourth short-circuit branch are all arranged along the first direction, the first microstrip line, the second microstrip line, the third microstrip line and the fourth microstrip line are all arranged along the second direction, and the first direction is perpendicular to the second direction.
2. The microstrip bandpass filter topology structure according to claim 1, characterized in that: The odd-mode characteristic impedance of the first three parallel lines is equal to the odd-mode characteristic impedance of the second three parallel lines, and the even-mode characteristic impedance of the first three parallel lines is equal to the even-mode characteristic impedance of the second three parallel lines.
3. The microstrip bandpass filter topology structure according to claim 1, characterized in that: The characteristic impedance of the first microstrip line, the characteristic impedance of the second microstrip line, the characteristic impedance of the third microstrip line, the characteristic impedance of the fourth microstrip line, the characteristic impedance of the first short-circuit branch, the characteristic impedance of the second short-circuit branch, the characteristic impedance of the third short-circuit branch and the characteristic impedance of the fourth short-circuit branch are equal.
4. The microstrip bandpass filter topology structure according to claim 2, characterized in that: The electrical length of the first parallel line, the electrical length of the first three parallel lines, and the electrical length of the second three parallel lines are equal, and are all equal to a quarter wavelength corresponding to the center frequency of the broadband bandpass filter.
5. The microstrip bandpass filter topology structure according to claim 4, characterized in that: The electrical length of the first microstrip line is equal to the electrical length of the fourth microstrip line; the electrical length of the second microstrip line is equal to the electrical length of the third microstrip line.
6. The microstrip bandpass filter topology structure according to claim 5, characterized in that: The electrical length of the first short-circuit branch is equal to the electrical length of the fourth short-circuit branch; the electrical length of the second short-circuit branch is equal to the electrical length of the third short-circuit branch.
7. The microstrip bandpass filter topology structure according to claim 6, characterized in that: The sum of the electrical length of the first microstrip line and the electrical length of the first short-circuit branch, the sum of the electrical length of the second microstrip line and the electrical length of the second short-circuit branch, the sum of the electrical length of the third microstrip line and the electrical length of the third short-circuit branch, and the sum of the electrical length of the fourth microstrip line and the electrical length of the fourth short-circuit branch are equal, and are all greater than one-quarter wavelength corresponding to the center frequency of the broadband bandpass filter.
8. A filter, characterized in that: It comprises the microstrip bandpass filter topology structure described in any one of claims 1 to 7.
9. The filter according to claim 8, characterized in that The filter further includes a circuit board, and the topological structure is integrated on the circuit board.
10. The filter according to claim 9, characterized in that The lengths of the first three parallel lines and the second three parallel lines are equal and are set to l T ; The spacing between the transmission lines constituting the first parallel three lines or the second parallel three lines is equal, set to s T The width of the transmission lines constituting the first three parallel lines or the second three parallel lines is equal, set to w T ; The length of the first parallel line is set to l p ; The spacing between the transmission lines constituting the first parallel line is set to s p ; The width of the transmission lines constituting the first parallel line is set to w p ; The lengths of the first microstrip line and the fourth microstrip line are equal, set to l1; the lengths of the first short-circuit branch and the fourth short-circuit branch are equal, set to l2; the lengths of the second microstrip line and the third microstrip line are equal, set to l3; the lengths of the second short-circuit branch and the third short-circuit branch are equal, set to l4; The width of the first microstrip line, the width of the second microstrip line, the width of the third microstrip line, the width of the fourth microstrip line, the width of the first short-circuit branch, the width of the second short-circuit branch, the width of the third short-circuit branch and the width of the fourth short-circuit branch are equal and set to w1.