Dual-passband filter based on dual-mode ring resonator and comprehensive design method thereof
By adopting dual-mode ring resonators and parallel short-circuit stubs in dual-pass band filters, the problems of complex design and insufficient frequency selectivity of existing dual-pass band filters are solved, and the dual-pass band characteristics and high frequency selectivity are achieved.
Patent Information
- Application Number
- CN202411809989.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-10
- Publication Date
- 2025-03-11
- Estimated Expiration
- 2044-12-10
AI Technical Summary
The existing dual-pass band filters are complex in design, large in size, and it is difficult to effectively improve the frequency selectivity of the communication system under limited frequency band resources.
The design method based on the dual-mode ring resonator is adopted, and a dual-mode ring resonator is formed through parallel coupling lines to achieve a phase difference of 180°, and a transmission zero point is introduced, combining parallel short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit short-circuit
The dual-pass band characteristic is realized, which improves frequency selectivity, simplifies the design process, reduces workload, and improves design efficiency.
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Figure CN119601928A_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to the technical field of radio frequency microwave filters, and in particular to a dual-passband filter based on a dual-mode ring resonator and a design method thereof. Background Art
[0002] In recent years, with the increasing demand for wireless communications, various wireless communication technologies have emerged. As an indispensable part of the communication system, filters play an important role in selecting the required frequency signals and filtering out interference signals. Their performance directly affects the performance of the entire wireless communication system. However, due to the limited available spectrum resources, single-band bandpass filters can no longer meet the needs of wireless communications. Compared with single-band bandpass filters, dual-band bandpass filters have multiple communication bands that can work simultaneously in the communication system, which fully utilizes the existing spectrum and basic equipment resources, and can greatly reduce the system size and improve system reliability. Therefore, in-depth research on the design principles of dual-band filters and the development of new filter topologies have important academic research and engineering application value.
[0003] In the past few years, people have conducted in-depth research on dual-passband filters. One of the direct design methods to achieve this is to connect two single-band bandpass filters in parallel. By sharing the same input and output ports, resonators that resonate at different frequencies are connected in parallel, and their matching circuits are designed to achieve their multi-frequency selectivity. Although this design method is intuitive, the parallel connection of multiple resonators makes the filter circuit larger in size and the design process of the matching network is more complicated. Another design method is to combine the broadband bandpass filter response with the bandstop filter response. The broadband bandpass filter provides a transmission pole to generate a wide passband, and the bandstop filter introduces a transmission zero to insert a stopband between the wide passband, thereby forming a dual-passband filter circuit.
[0004] Although the above method provides a detailed design process, it still requires continuous debugging and trial and error to obtain a good filtering response result. In addition, under limited frequency band resources, increasing the transmission zero point and improving the frequency selectivity of the dual-passband filter can further effectively improve the performance of the communication system and has broad application prospects. Summary of the invention
[0005] Therefore, an object of the present invention is to provide a dual-passband filter based on a dual-mode ring resonator and a design method thereof to solve the problems in the background technology.
[0006] A dual-passband filter based on a dual-mode ring resonator, comprising a dielectric substrate (13), a microstrip line structure (14) printed on the upper surface of the dielectric substrate (13), and a metal grounding plate (15) on the lower surface of the dielectric substrate (13);
[0007] The microstrip line (14) structure comprises an input feeder (1), an output feeder (2), a first cascade transmission line (3) connecting the input feeder (1) and a first vertical parallel coupling line (5), a second cascade transmission line (4) connecting the output feeder (2) and a second vertical parallel coupling line (6), an upper lateral cascade transmission line (7) and a lower lateral cascade transmission line (8) respectively connecting the first vertical parallel coupling line (5) and the second vertical parallel coupling line (6), a first vertical parallel short-circuit stub (9) located between the input feeder (1) and the first cascade transmission line (3), a second vertical parallel short-circuit stub (10) located between the second output feeder (2) and the second cascade transmission line (4), a V-shaped first open-circuit stub (11) located between the first cascade transmission line (3) and the first vertical parallel coupling line (5), and a second open-circuit stub (12) located between the second cascade transmission line (4) and the second vertical parallel coupling line (6);
[0008] The first vertical parallel coupling line (5), the second vertical parallel coupling line (6), and the upper lateral cascade transmission line (7) and the lower lateral cascade transmission line (8) respectively connecting the two constitute a dual-mode ring resonator; wherein the first vertical parallel coupling line (5), the second vertical parallel coupling line (6) and the upper lateral transmission line (7) constitute a signal path, and the lower lateral transmission line (8) serves as another signal path, and signal cancellation is achieved through a phase difference of 180°, thereby generating three transmission zero points in the middle of a wide passband.
[0009] Furthermore, the electrical length of the structure of the first open-circuit stub (11), the second open-circuit stub (12), the upper lateral cascade transmission line (7) and the lower lateral cascade transmission line (8) is half a wavelength, so as to reduce the size.
[0010] Furthermore, the electrical lengths of the remaining transmission line structures except the first open-circuit stub (11), the second open-circuit stub (12), the upper lateral cascade transmission line (7) and the lower lateral cascade transmission line (8) are all one-quarter wavelength.
[0011] Furthermore, the first cascade transmission line (3) and the second cascade transmission line (4), the first vertical parallel coupling line (5) and the second vertical parallel coupling line (6), the first vertical parallel short-circuit stub (9) and the second vertical parallel short-circuit stub (10), and the first open-circuit stub (11) and the second open-circuit stub (12) of the V-shaped structure have consistent structural parameters.
[0012] Furthermore, the first parallel open stub (11) and the second parallel open stub (12) are parallel to each other and extend in the same direction, and the extension direction of the first parallel open stub (11) is opposite to the extension direction of the first perpendicular parallel coupling line (5).
[0013] Furthermore, the first vertical parallel short-circuit stub (9) and the second vertical parallel short-circuit stub (10) are arranged in parallel and extend in the same direction, and the first vertical parallel short-circuit stub (9) is parallel to the first vertical parallel coupling line (5).
[0014] A comprehensive design method for a dual-passband filter based on a dual-mode ring resonator, firstly establishing a transmission line model, wherein the transmission line model comprises a pair of cascaded transmission lines (Z1, θ), a pair of parallel coupled lines (Z0e1, Z0o1, θ), transmission lines (Za1, 2θ) and (Za2, 2θ) connecting the parallel coupled lines, a pair of parallel short-circuited stubs (Zb1, θ) and a pair of parallel open-circuited stubs (Zb2, 2θ); wherein the electrical length θ is equal to a quarter wavelength;
[0015] The transmission line model of the proposed dual-passband filter is divided into panels along the symmetry plane using the odd-even mode analysis method, and the scattering parameters are expressed as:
[0016]
[0017] The filter function is expressed as:
[0018]
[0019] Select Chebyshev response as the filter response type, and the n-order filter function is expressed as:
[0020]
[0021] in,
[0022]
[0023] Ω1 and Ω2 are the lower cutoff frequency and upper cutoff frequency of the filter function, respectively, and γk is the position of the transmission zero point;
[0024] The single-band response is converted to a dual-band response by using the Richards transformation jΩ=jtanθ;
[0025]
[0026] θ2 and θ2' are the upper and lower edge frequencies of the outermost sides of the dual passband respectively;
[0027] The calculated transfer function of the dual-passband filter and the target filter function are used to establish a loss function. After continuous iteration, the optimal electrical parameters of the circuit can be quickly obtained.
[0028]
[0029] Furthermore, the transmission line model is verified by three-dimensional electromagnetic simulation.
[0030] Preferably, the impedance of the input and output feeder lines is set to 50Ω.
[0031] Preferably, a transition structure is used at the connection parts between the first cascade transmission line, the second cascade transmission line and the dual-mode ring resonator.
[0032] In summary, the present invention uses a dual-mode ring resonator to achieve a phase difference of 180°, so as to introduce a transmission zero in the middle of a wide passband to achieve dual passband characteristics, and uses parallel coupled lines to design the ring resonator to achieve multiple transmission poles. And by connecting a half-wavelength open-circuit stub in parallel, a transmission zero can be added to the lower stopband and the upper stopband of the dual passband, respectively, greatly improving the frequency selectivity. A comprehensive design method is adopted to perform frequency conversion from a single passband to a dual passband, and a loss function is designed using a transfer function and a suitable selected filter function, so that the optimal electrical parameters that meet the design indicators of the dual passband filter can be quickly obtained, effectively improving the design efficiency and reducing the workload.
[0033] In addition, the present invention adopts a compact microstrip line structure, which has the advantages of low cost, mature processing technology, and easy integration in realizing multi-band filtering functions. The ring resonator is designed to realize multiple transmission zeros and transmission poles, improve the out-of-band suppression capability of the filter, and effectively obtain the required useful signals, which is beneficial to solving the problem of increasingly tight communication spectrum and has broad application prospects. BRIEF DESCRIPTION OF THE DRAWINGS
[0034] Figure 1 A schematic diagram of the structure of the dual-passband filter proposed by the present invention;
[0035] Figure 2 for Figure 1 Schematic diagram of the structure of the microstrip line;
[0036] Figure 3 A transmission line model of the dual-passband filter proposed by the present invention;
[0037] Figure 4 The even-odd mode equivalent circuit of the dual-passband filter proposed by the present invention;
[0038] Figure 5 The comprehensive theoretical frequency response of the dual-passband filter proposed by the present invention;
[0039] Figure 6 A schematic diagram of the layout of the dual-passband filter proposed in the present invention;
[0040] Figure 7 This is the electromagnetic simulation result of the dual-passband filter proposed in the present invention.
[0041] Reference numerals:
[0042] Dielectric substrate 13 Microstrip line 14 Metal ground plate 15 Input feed line 1 Output feed line 2
[0043] First cascade transmission line 3 Second cascade transmission line 4 First vertical parallel coupling line 5
[0044] Second vertical parallel coupling line 6 Upper lateral cascade transmission line 7 Lower lateral cascade transmission line 8
[0045] First parallel short-circuited stub 9 Second parallel short-circuited stub 10 First parallel open-circuited stub 11
[0046] The second parallel open circuit stub 12 DETAILED DESCRIPTION
[0047] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
[0048] like Figure 1 and Figure 2 As shown, the present invention provides a dual-passband filter based on a dual-mode ring resonator, which includes a dielectric substrate 13, a microstrip line 14 arranged on the upper surface of the dielectric substrate 13, and a metal ground plate 15 on the lower surface of the dielectric substrate 13. In this embodiment, the microstrip line 14 is printed on the dielectric substrate 13; the dielectric substrate 13 is a high-frequency board, and its relative dielectric constant ε r =2.55, the thickness of the dielectric substrate 13 is 1 mm. The dielectric substrate 13 is closely attached to the microstrip line 14 and the metal ground plane 15 respectively.
[0049] The microstrip line 14 structure is a symmetrical structure, which includes an input feeder 1, an output feeder 2, a first cascade transmission line 3, a second cascade transmission line 4, a first vertical parallel coupling line 5, a second vertical parallel coupling line 6, an upper lateral cascade transmission line 7, a lower lateral cascade transmission line 8, a first vertical parallel short-circuit stub 9, a second vertical parallel short-circuit stub 10, a first open stub 11 and a second open stub 12. In this embodiment, the input feeder 1 and the output feeder 2 are both 50Ω impedance line width; the electrical length of the first open stub 11, the second open stub 12, the upper lateral cascade transmission line 7 and the lower lateral cascade transmission line 8 is half a wavelength; and the electrical lengths of the other transmission line structures are all quarter wavelengths.
[0050] The first cascade transmission line 3 is connected to the input feeder 1 and the first vertical parallel coupling line 5, and the second cascade transmission line 4 is connected to the output feeder 2 and the second vertical parallel coupling line 6. The upper lateral cascade transmission line 7 and the lower lateral cascade transmission line 8 are arranged between the first vertical parallel coupling line 5 and the second vertical parallel coupling line 6, and are connected to the first vertical parallel coupling line 5 and the second vertical parallel coupling line 6, respectively.
[0051] The first vertical parallel short-circuit stub 9 is located between the input feeder 1 and the first cascade transmission line 3, and the second vertical parallel short-circuit stub 10 is located between the output feeder 2 and the second cascade transmission line 4. The first open-circuit stub 11 and the second open-circuit stub 12 are both arranged in a V shape, and the first open-circuit stub 11 is located between the first cascade transmission line 3 and the first vertical parallel coupling line 5; the second open-circuit stub 12 is located between the second cascade transmission line 4 and the second vertical parallel coupling line 6. In this embodiment, the first vertical parallel short-circuit stub 9, the second vertical parallel short-circuit stub 10 and the first vertical parallel coupling line 5 and the second vertical parallel coupling line 6 are all arranged on the same side of the cascade transmission line, while the first open-circuit stub 11 and the second open-circuit stub 12 are arranged on the other side of the cascade transmission line.
[0052] The first vertical parallel coupling line 5, the second vertical parallel coupling line 6, the upper lateral cascade transmission line 7 and the lower lateral cascade transmission line 8 form a dual-mode ring resonator, and the dual-mode ring resonator can generate three transmission zeros (such as Figure 5 The parallel connection of the half-wavelength V-shaped first open circuit stub 11 and the second open circuit stub 12 can add a pair of transmission zeros on both sides of the dual passband (such as Figure 5 The position of the transmission zero point can be controlled by adjusting its size.
[0053] The first vertical parallel coupling line 5, the second vertical parallel coupling line 6 and the upper horizontal cascade transmission line 7 form a signal path, and the lower horizontal cascade transmission line 8 serves as another signal path; signal cancellation is achieved through a 180° phase difference to achieve dual-band characteristics. The position of the transmission zero point can be flexibly controlled by adjusting the coupling coefficient of the first parallel coupling line 5 and the second parallel coupling line 6. The dual-mode ring resonator and the parallel first open short stub 11 and the second open short stub 12 can achieve seven transmission zero points (such as Figure 5 ), effectively improving the frequency selectivity.
[0054] like Figure 3 As shown, the transmission line model of the dual-passband filter proposed in the present invention is composed of a pair of cascaded transmission lines (Z1, θ), a pair of parallel coupled lines (Z0e1, Z0o1, θ), transmission lines (Za1, 2θ) and (Za2, 2θ) connecting the parallel coupled lines, a pair of parallel short-circuited stubs (Zb1, θ) and a pair of parallel open-circuited stubs (Zb2, 2θ). The electrical length θ is equal to a quarter wavelength.
[0055] The transmission line model of the proposed dual-passband filter is analyzed along the symmetry plane using the odd-even mode analysis method; (e.g. Figure 4 As shown, it is the odd-even mode equivalent circuit of the proposed dual-passband filter);
[0056] Among them, the scattering parameters (S11 is the return loss and S21 is the insertion loss) can be expressed as:
[0057]
[0058] The filter function can be expressed as:
[0059]
[0060] Select Chebyshev response as the filter response type, and the n-order filter function can be expressed as:
[0061]
[0062] in,
[0063]
[0064] Ω1 and Ω2 are the lower cutoff frequency and upper cutoff frequency of the filter function, respectively, and γk is the position of the transmission zero point.
[0065] The single-band response is converted to a dual-band response by using the Richards transform jΩ=jtanθ
[0066]
[0067] θ2 and θ2' are the upper edge frequency and the lower edge frequency of the outermost side of the dual passband respectively.
[0068] The calculated transfer function of the dual-passband filter and the target filter function are used to establish a loss function. After continuous iteration, the optimal electrical parameters of the circuit can be quickly obtained.
[0069]
[0070] Through calculation, in this example, the design parameters are selected as follows: Z1 = 35.1Ω, Z0e1 = 123.4Ω, Z0o1 = 43.9Ω, Zb1 = 91.2Ω, Zb2 = 134.7Ω, Za1 = 87.9Ω, Za2 = 99.5Ω. And the comprehensive theoretical frequency response structure is as follows Figure 5 As shown, the results show that the center frequency of the first passband is 2.44GHz, the operating frequency range is 2.18~2.71GHz, and the return loss in the first passband is less than -17.34dB. The center frequency of the second passband is 5.55GHz, the operating frequency range is 5.28~5.83GHz, and the return loss in the second passband is less than -17.11dB. And it can be clearly observed that there are seven transmission zeros outside the passband, which effectively improves the frequency selectivity.
[0071] From the above, it can be seen that in order to improve the design efficiency, a comprehensive design method is adopted. By analyzing the circuit characteristics of the proposed dual-passband filter, the ideal Chebyshev transfer function is used as the optimization objective function, and the loss function is designed using the transfer function and the selected appropriate filter function. The minimum mean square error optimization iteration is performed, and the optimal characteristic impedance value that meets the design indicators of the dual-passband filter can be quickly obtained.
[0072] like Figure 6 The figure shows the layout of the dual-passband filter proposed by the present invention, and illustrates the final physical size in mm. The size of the entire dual-passband filter is 42 mm×85 mm.
[0073] The tunable filter attenuator proposed in the present invention is composed of a dielectric substrate, a microstrip line printed on the upper surface of the dielectric substrate, and a metal ground plane on the lower surface. Specifically, the dielectric substrate is a rectangular parallelepiped with a solid dielectric inside. This example uses the dielectric substrate material of Arlon AD255A, whose relative dielectric constant ε r =2.55, the thickness of the dielectric substrate is 1mm. The upper and lower layers of the dielectric substrate are closely attached to the microstrip line and the metal ground plane respectively.
[0074] like Figure 7As shown in the figure, it is the electromagnetic simulation result of the three-dimensional electromagnetic simulation verification of the dual-passband filter; the result shows that the center frequency of the first passband is 2.28GHz, the operating frequency range is 2.04~2.53GHz, the return loss S11 in the first passband is less than -10.8dB, and the insertion loss S21 is greater than -0.59dB. The center frequency of the second passband is 5.03GHz, the operating frequency range is 4.83~5.23GHz, and the return loss S11 in the second passband is less than -11.33dB, and the insertion loss S21 is greater than -0.78dB.
[0075] In summary, the present invention is provided with a dielectric substrate, input and output feeders located on the top layer of the dielectric substrate, two sections of cascaded transmission lines connecting the input and output feeders and a dual-mode ring resonator, vertical parallel short-circuit stubs and bent parallel open-circuit stubs, and a metal grounding plate located on the bottom layer of the dielectric substrate. The ring resonator is composed of a pair of vertical coupling lines and two sections of lateral transmission lines. The two coupling lines and the lateral transmission line on the upper side form a signal path, while the lateral transmission line on the lower side serves as another signal path, and signal cancellation is achieved through a phase difference of 180°, thereby achieving dual-band characteristics. And by using the dual-mode ring resonator and the parallel open-circuit stubs, seven transmission zeros can be achieved, which effectively improves the frequency selectivity. In addition, the present invention also provides a comprehensive design method, which can obtain the optimal characteristic impedance value, fully improve the design efficiency, and has universality; it is highly practical and has a strong promotion significance.
[0076] The above-mentioned embodiment only expresses one implementation mode of the present invention, and its description is relatively specific and detailed, but it cannot be understood as limiting the scope of the patent of the present invention. It should be pointed out that for ordinary technicians in this field, several modifications and improvements can be made without departing from the concept of the present invention, which all belong to the protection scope of the present invention. Therefore, the protection scope of the patent of the present invention shall be based on the attached claims.
Claims
1. A dual-passband filter based on a dual-mode ring resonator, characterized in that: It comprises a dielectric substrate (13), a microstrip line structure (14) printed on the upper surface of the dielectric substrate (13), and a metal grounding plate (15) on the lower surface of the dielectric substrate (13); The microstrip line (14) structure comprises an input feeder (1), an output feeder (2), a first cascade transmission line (3) connecting the input feeder (1) and a first vertical parallel coupling line (5), a second cascade transmission line (4) connecting the output feeder (2) and a second vertical parallel coupling line (6), an upper lateral cascade transmission line (7) and a lower lateral cascade transmission line (8) respectively connecting the first vertical parallel coupling line (5) and the second vertical parallel coupling line (6), a first vertical parallel short-circuit stub (9) located between the input feeder (1) and the first cascade transmission line (3), a second vertical parallel short-circuit stub (10) located between the second output feeder (2) and the second cascade transmission line (4), a V-shaped first open-circuit stub (11) located between the first cascade transmission line (3) and the first vertical parallel coupling line (5), and a second open-circuit stub (12) located between the second cascade transmission line (4) and the second vertical parallel coupling line (6); The first vertical parallel coupling line (5), the second vertical parallel coupling line (6), and the upper lateral cascade transmission line (7) and the lower lateral cascade transmission line (8) respectively connecting the two constitute a dual-mode ring resonator; wherein the first vertical parallel coupling line (5), the second vertical parallel coupling line (6) and the upper lateral transmission line (7) constitute a signal path, and at the same time, the lower lateral transmission line (8) serves as another signal path, and realizes signal cancellation through a phase difference of 180°, thereby generating three transmission zero points in the middle of a wide passband.
2. The dual-passband filter based on a dual-mode ring resonator according to claim 1, characterized in that: The electrical length of the structure of the first open-circuit stub (11), the second open-circuit stub (12), the upper lateral cascade transmission line (7) and the lower lateral cascade transmission line (8) is half a wavelength.
3. The dual-passband filter based on a dual-mode ring resonator according to claim 2, characterized in that: The electrical lengths of the remaining transmission line structures except the first open-circuit stub (11), the second open-circuit stub (12), the upper lateral cascade transmission line (7) and the lower lateral cascade transmission line (8) are all one-quarter wavelength.
4. The dual-passband filter based on a dual-mode ring resonator according to claim 1, characterized in that: The first cascade transmission line (3) and the second cascade transmission line (4), the first vertical parallel coupling line (5) and the second vertical parallel coupling line (6), the first vertical parallel short-circuit stub (9) and the second vertical parallel short-circuit stub (10), and the first open-circuit stub (11) and the second open-circuit stub (12) of the V-shaped structure have consistent structural parameters.
5. The dual-passband filter based on a dual-mode ring resonator according to claim 1, characterized in that: The first parallel open-circuit stub (11) and the second parallel open-circuit stub (12) are parallel to each other and extend in the same direction, and the extension direction of the first parallel open-circuit stub (11) is opposite to the extension direction of the first perpendicular parallel coupling line (5).
6. The dual-passband filter based on a dual-mode ring resonator according to claim 5, characterized in that: The first vertical parallel short-circuit stub (9) and the second vertical parallel short-circuit stub (10) are arranged in parallel and extend in the same direction, and the first vertical parallel short-circuit stub (9) is parallel to the first vertical parallel coupling line (5).
7. The dual-passband filter based on a dual-mode ring resonator according to claim 5, characterized in that: The connection parts between the first cascade transmission line (3), the second cascade transmission line (4) and the dual-mode ring resonator use a transition structure.
8. A comprehensive design method for a dual-passband filter based on a dual-mode ring resonator, characterized in that: A transmission line model is established, wherein the transmission line model includes a pair of cascaded transmission lines (Z1, θ), a pair of parallel coupled lines (Z0e1, Z0o1, θ), transmission lines (Za1, 2θ) and (Za2, 2θ) connecting the parallel coupled lines, a pair of parallel short-circuited stubs (Zb1, θ) and a pair of parallel open-circuited stubs (Zb2, 2θ); wherein the electrical length θ is equal to a quarter wavelength; The transmission line model of the proposed dual-passband filter is calculated and analyzed along the symmetry plane using the odd-even mode analysis method, and the scattering parameters are expressed as: The filter function is expressed as: Select Chebyshev response as the filter response type, and the n-order filter function is expressed as: in, Ω1 and Ω2 are the lower cutoff frequency and upper cutoff frequency of the filter function, respectively, and γk is the position of the transmission zero point; The single-band response is converted to a dual-band response by using the Richards transformation jΩ=jtanθ; θ2 and θ2' are the upper and lower edge frequencies of the outermost sides of the dual passband respectively; The calculated transfer function of the dual-passband filter and the target filter function are used to establish a loss function to quickly obtain the optimal electrical parameters of the circuit; 9. The comprehensive design method of a dual-passband filter based on a dual-mode ring resonator according to claim 8, characterized in that: The transmission line model also needs to be verified by three-dimensional electromagnetic simulation.
Citation Information
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