Multi-absorption-band ultra-wideband common-mode filter based on mixed resonator structure

By adopting a hybrid resonator structure and multi-absorbing band design in the common mode filter, the problems of narrow absorption bandwidth and common mode noise reflection in the prior art are solved, and the ultra-wideband common mode rejection and multi-absorbing band effects are achieved, ensuring signal integrity and electromagnetic compatibility.

CN119651097AActive Publication Date: 2025-03-18SOUTHEAST UNIV

Patent Information

Application Number
CN202510147549.1
Authority / Receiving Office
CN · China
Patent Type
Applications(China)
Current Assignee / Owner
Filing Date
2025-02-11
Publication Date
2025-03-18
Estimated Expiration
2045-02-11

AI Technical Summary

Technical Problem

When existing common mode filters absorb common mode noise, the absorption bandwidth is narrow, which cannot meet the wide frequency requirements of the differential signal spectrum in high-speed circuits. At the same time, common mode noise reflected back to the previous stage will increase the signal bit error rate and reduce the amplifier stability.

Method used

A multi-absorbing band ultra-wideband common mode filter based on a hybrid resonator structure is adopted. By coupling the combination of microstrip lines, main resonators, secondary resonators and resistors, hybrid resonance and multi-absorbing bands are achieved, and the common mode rejection band and absorption bandwidth are widened.

Benefits of technology

It realizes common mode noise suppression for application systems such as ultra-wideband communication, reduces the interference of common mode noise on differential signals, and avoids echo electromagnetic interference, ensuring the normal transmission of differential mode signals.

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Abstract

The invention relates to a multi-absorption-band ultra-wideband common-mode filter based on a mixed resonator structure. The multi-absorption-band ultra-wideband common-mode filter comprises a coupling microstrip line, a dielectric substrate, a main resonator, an auxiliary resonator and a resistor, the filter has an upper surface and a lower surface, and a coupling microstrip line comprises a metal conduction band located on a dielectric substrate and a metal ground layer located below the dielectric substrate; two ends of the coupling microstrip line are respectively connected with the input port and the output port; the main resonator is etched in the middle of the metal ground layer; the auxiliary resonator is etched on the outer side of the main resonator in the metal ground layer; the coupling microstrip line is mutually coupled with the main resonator and the auxiliary resonator to realize mixed resonance; the resistor crosses the gap of the auxiliary resonator at the intersection of the auxiliary resonator and the symmetric line, and the two ends of the resistor are connected with the metal ground layers inside and outside the metal conduction band; according to the invention, the ultra-wideband common-mode suppression bandwidth and a plurality of absorption bands are provided, and the absorption bands dissipate common-mode noise in the form of heat energy, so that the problem of potential common-mode electromagnetic interference in the system is reduced, and normal transmission of differential-mode signals is not damaged at the same time.
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Description

Technical Field

[0001] The invention relates to a common mode filter technology, in particular to a multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure, belonging to the technical field of electromagnetic compatibility. Background Art

[0002] Differential signals are widely used in high-speed and radio frequency circuit systems. However, due to path asymmetry, amplitude imbalance, time skew and other reasons in the circuit, common-mode noise is easily caused in the circuit. Common-mode noise and differential-mode signals are converted to each other, causing problems such as increased signal bit error rate and increased spurious spectrum. Common-mode filters are used to suppress common-mode noise while ensuring the normal transmission of differential-mode signals.

[0003] Existing common-mode filters are usually reflective, which reflect common-mode noise back to the previous stage to eliminate the impact of common-mode noise on the subsequent circuit. However, the common-mode noise reflected back to the previous stage will still cause problems such as increased signal bit error rate of the previous circuit and decreased amplifier stability. Absorptive common-mode filters can dissipate common-mode noise in the form of heat energy, but the existing absorptive common-mode filters have a narrow absorption bandwidth and cannot achieve broadband common-mode noise absorption. The spectrum of differential signals in high-speed circuits usually covers a wide frequency range. Therefore, it is hoped that the absorption bandwidth of the absorptive common-mode filter is wide enough. Summary of the invention

[0004] Technical problem: The present invention proposes a multi-absorption-band ultra-wideband common-mode filter based on a hybrid resonator structure. The common-mode suppression bandwidth of the filter is wide, and it has a protective effect on application systems such as ultra-wideband communications. The filter has multiple absorption bands, which can absorb and suppress common-mode noise in a wider bandwidth, and reduce the interference of common-mode noise on differential signals, while not generating echo electromagnetic interference.

[0005] Technical solution: A multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure of the present invention comprises a coupled microstrip line, a dielectric substrate, a main resonator, a sub-resonator, and a resistor; the filter has an upper and lower surface, the coupled microstrip line comprises a metal conduction band located on the dielectric substrate and a metal stratum located below the dielectric substrate; one end of the coupled microstrip line is connected to an input port, and the other end is connected to an output port; the main resonator is etched in the middle of the metal stratum; the sub-resonator is etched on the outside of the main resonator in the metal stratum; the metal conduction band is located in the main resonator, the coupled microstrip line is coupled with the main resonator and the sub-resonator to realize hybrid resonance; the resistor is at the intersection of the sub-resonator and the symmetry line, spanning the gap of the sub-resonator, and the two ends of the resistor are respectively connected to the metal stratum inside the metal conduction band and the metal stratum outside the metal conduction band.

[0006] The coupled microstrip lines are symmetrically distributed about the symmetry line, and the middle part is a wavy structure with multiple bends; changing the shape characteristics or length of the bends can adjust the common mode suppression frequency range and suppression degree.

[0007] The main resonator includes short-circuit slot line branches, main slot lines, and connecting slot lines, and are symmetrically distributed about the symmetry line; the short-circuit slot line branches are arranged in sequence from the input port to the output port and are connected to the main slot line of the main resonator, and the connecting slot line is located at the end of the main slot line and on the side close to the output port, connecting the main slot lines on both sides of the symmetry line; changing the number or spacing distance of the short-circuit slot line branches can adjust the common-mode suppression band and suppression strength.

[0008] The sub-resonators are symmetrically distributed about the symmetry line, the upper and lower sides of the sub-resonators are wavy structures with multiple bends, and the upper and lower sides of the sub-resonators are connected on the input port side; adjusting the length and shape characteristics of the sub-resonator can adjust the common mode suppression degree and adjust the common mode transmission coefficient S CC21 The number of absorption bands within the common mode rejection bandwidth less than -10 dB, divided by the common mode transmission coefficient S CC21 In addition to the common-mode rejection bandwidth of less than -10dB, there are also absorption bands at higher frequencies.

[0009] The loaded resistor is the main component for absorbing common-mode noise, and its resistance is equal to the common-mode input impedance; the resistor is a chip resistor, a ceramic resistor, a carbon film resistor or a chip resistor.

[0010] Changing the resistor package size can adjust the resistor's parasitic effects and power handling.

[0011] The coupled microstrip line is used as a transmission line for differential signals. By changing the line width and line spacing of the metal conducting strip in the coupled microstrip line, the differential mode and common mode characteristic impedances can be adjusted.

[0012] In the coupled microstrip line, the wavy structure of the metal conducting strip that is bent multiple times is an arc, a 45° angle, and a right angle.

[0013] In the sub-resonator, the wave-like structures with multiple bends on the upper and lower sides are arcs, circles, or triangles.

[0014] When the common-mode filter inputs a differential signal, the short-circuited slot line branches on the main resonator increase the current path length, which equivalently increases the distributed inductance of the slot line transmission line, thereby improving the characteristic impedance of the slot line transmission line, and the coupled microstrip line and the main resonator are in series resonance to obtain an ultra-wideband suppression bandwidth, thereby realizing the reflection of the common-mode component in the differential signal, and at the resonance point, the real part and the imaginary part of the even-mode input impedance of the series resonance network composed of the coupled microstrip line and the main resonance are both zero; the loading of the sub-resonator causes the coupled microstrip line to couple with the main and sub-resonators to realize hybrid resonance, thereby further widening the reflection bandwidth; the loading of the resistor with a suitable resistance value enables the entire common-mode filter to achieve common-mode input impedance matching at certain specific frequency points, realize multiple absorption bands, greatly widen the absorption bandwidth, and the common-mode noise is absorbed instead of being reflected back to the previous stage.

[0015] Beneficial effects: The present invention proposes a multi-absorption band ultra-wideband common-mode filter based on a hybrid resonator structure, which bends the metal conduction band to increase the coupling strength between the metal conduction band and the resonator; uses the spaced slot line branches to increase the current path length, thereby increasing the characteristic impedance of the main resonator and shifting the resonant frequency to a low frequency, effectively widening the common-mode suppression bandwidth; uses a main resonator and a sub-resonator, and couples the microstrip line and the main and sub-resonators to each other to achieve hybrid resonance and ultra-wideband common-mode suppression performance; uses a sub-resonator and a resistor to achieve common-mode input impedance matching in multiple frequency bands, thereby achieving multiple absorption bands and widening the absorption bandwidth.

[0016] The present invention not only realizes the common-mode suppression performance of ultra-wideband, but also does not destroy the signal integrity of the differential-mode signal, thereby ensuring the normal transmission of the differential-mode signal.

[0017] The present invention bends the metal conduction strip and the sub-resonator to realize miniaturized design.

[0018] The present invention has a simple structure, is conducive to low-cost production and implementation, and is conducive to integration into a radio frequency microwave circuit system and a high-speed circuit system.

[0019] The filter has a wide common-mode suppression bandwidth and has a protective effect on application systems such as ultra-wideband communications. The filter has multiple absorption bands, which can absorb and suppress common-mode noise in a wider bandwidth and reduce the interference of common-mode noise on differential signals without generating echo electromagnetic interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 It is a structural schematic diagram of a multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure provided by an embodiment of the present invention.

[0021] Figure 2It is a schematic diagram of the top and bottom surfaces of a multi-absorption-band ultra-wideband common-mode filter based on a hybrid resonator structure provided in an embodiment of the present invention, wherein (a) is the upper surface and (b) is the lower surface.

[0022] Figure 3 It is a schematic diagram of an even-mode equivalent circuit of a multi-absorption-band ultra-wideband common-mode filter based on a hybrid resonator structure provided by an embodiment of the present invention.

[0023] Figure 4 The present invention provides a hybrid resonator structure-based multi-absorption band ultra-wideband common mode filter provided by an embodiment of the present invention, which only includes a coupled microstrip line and a main resonator structure.

[0024] Figure 5 This is the measured result of mixed-mode scattering parameters of the overall structure of a multi-absorption-band ultra-wideband common-mode filter based on a hybrid resonator structure provided by an embodiment of the present invention.

[0025] Figure 6 This is the measured result of the absorption rate of the overall structure of a multi-absorption-band ultra-wideband common-mode filter based on a hybrid resonator structure provided by an embodiment of the present invention.

[0026] Figure 7 This is an actual measured eye diagram result of a multi-absorption-band ultra-wideband common-mode filter based on a hybrid resonator structure provided by an embodiment of the present invention when the transmission rate is 10 Gbps differential mode signal. The actual measured result is a test result directly output by a four-port vector network analyzer, wherein the horizontal axis represents time, and the starting range is -100 picoseconds to +100 picoseconds; wherein the vertical axis represents voltage, and the starting range is -2.5 volts to +2.5 volts.

[0027] The figure includes: a coupled microstrip line 1, a metal guide strip 11, a metal ground layer 12, a dielectric substrate 2, a main resonator 3, a short-circuit slot line branch 31, a main slot line 32, a connecting slot line 33, a sub-resonator 4, a resistor 5, a symmetry line 6, an input port 71, and an output port 72. DETAILED DESCRIPTION

[0028] The specific implementation modes of the present invention are further described below in conjunction with the accompanying drawings and examples. The specific embodiments described herein are only used to explain the present invention, and the present invention cannot be limited by the specific embodiments.

[0029] For the sake of clarity and convenience in expression and description, Figure 1 and Figure 2 The structure of a multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure is described as a specific implementation method, and the present invention is not limited to this specific common mode filter structure.

[0030] The dual-absorption band ultra-wideband common mode filter adopted by the present invention comprises a coupled microstrip line 1, a dielectric substrate 2, a main resonator 3, a sub-resonator 4 and a resistor 5. The filter has an upper and lower surface, the coupled microstrip line 1 comprises a metal conductive strip 11 located on the dielectric substrate 2 and a metal ground layer 12 located below the dielectric substrate 2; one end of the coupled microstrip line 1 is connected to an input port 71, and the other end is connected to an output port 72; the main resonator 3 is etched in the middle of the metal ground layer 12; the sub-resonator 4 is etched outside the main resonator 3 in the metal ground layer 12; the metal conductive strip 11 is located in the main resonator 3, and the coupled microstrip line 1 is mutually coupled with the main resonator 3 and the sub-resonator 4; the resistor 5 is at the intersection of the sub-resonator 4 and the symmetry line 6, spanning the gap of the sub-resonator 4, and the two ends of the resistor 5 are connected to the metal ground layer 12 inside and outside the metal conductive strip 11.

[0031] The coupled microstrip line 1 is used as a transmission line for differential signals. The differential mode characteristic impedance of the coupled microstrip line 1 is 100 ohms, and the common mode characteristic impedance is 33 ohms. The differential signal is fed in from the input port 71 and fed out from the output port 72. The metal guide strip in the middle part of the coupled microstrip line 1 is bent 90° multiple times to increase the coupling strength with the resonator and enhance the suppression performance. The wavy structure with multiple bends can also be an arc, a 45° angle or a right angle.

[0032] The main resonator 3 is etched on the metal layer 12 and is symmetrically distributed about the symmetry line 6. The short-circuit slot line branches 31 are evenly spaced from the input port 71 to the output port 72 and are connected to the main slot line 32 of the main resonator 3. The connecting slot line 33 is located at the end of the main slot line 32 and close to the output port 72. The evenly spaced short-circuit slot line branches 31 are used to increase the current path length, thereby increasing the equivalent characteristic impedance of the resonator, and at the same time shift the resonant frequency to a low frequency, thereby achieving a better low-frequency suppression effect in a small-size structure, thereby achieving ultra-wideband common-mode suppression performance. Changing the number and spacing of the short-circuit slot line branches 31 can adjust the common-mode suppression band and suppression strength.

[0033] The sub-resonator 4 is symmetrically distributed about the symmetry line 6, and the upper and lower sides of the sub-resonator 4 are a wave-like structure with multiple bends, and the upper and lower sides of the sub-resonator 4 are connected on one side of the input port 71; adjusting the length and shape characteristics of the sub-resonator 4 can adjust the common mode suppression degree and adjust the common mode transmission coefficient S CC21 The number of absorption bands within the common mode rejection bandwidth less than -10 dB, divided by the common mode transmission coefficient S CC21In addition to the common mode suppression bandwidth less than -10dB, there are also absorption bands at higher frequencies; the coupled microstrip line 1 and the main resonator 3 and the sub-resonator 4 are coupled to each other, and the two resonators broaden the common mode suppression bandwidth and enhance the common mode suppression strength; the suppression strength and position distribution of multiple absorption bands can be adjusted by adjusting the shape characteristics and length of the sub-resonator 4. The wavy structure with multiple bends on the upper and lower sides can also be an arc, a circle or a triangle.

[0034] The resistor 5 is located on the symmetry line 6 of the metal layer 12. In this embodiment, a 0201 package and a 33ohm chip resistor are used to span the gap of the sub-resonator 4 and are welded on the metal layer at the intersection of the sub-resonator 4 and the symmetry line 6. The resistor 5 is the main component for absorbing common-mode noise, and its resistance is equal to the common-mode input impedance. The implementation form of the resistor 5 is not limited to the chip resistor, and a ceramic resistor, a carbon film resistor or a chip resistor can also be used.

[0035] Figure 3 The even-mode equivalent circuit of the embodiment of the present invention is described. The even-mode equivalent circuit is obtained by using the odd-even mode analysis method. When the common-mode signal is input, the symmetry plane perpendicular to the dielectric substrate 2 and intersecting the symmetry line 6 is an equivalent magnetic wall. Therefore, only the circuit structure on one side of the symmetry line 6 is analyzed to obtain Figure 2 The even-mode equivalent circuit described above; the embodiment of the present invention obtains the potential absorption band position by deriving and calculating the common-mode input impedance of the series network of the coupled microstrip line 1 and the main resonator 3, and matches the absorption band position by adjusting the length of the sub-resonator 4, and the loading resistor 5 can realize the absorption of common-mode noise. 1,even and θ1 represent the even-mode characteristic impedance and electrical length of the coupled microstrip line 1, respectively. 3,even and θ5 represent the even-mode characteristic impedance and electrical length of the slot line branch 31, respectively. 2,even Represents the even-mode characteristic impedance of the trunk line, θ 2、 θ3 is the electrical length of each segmented transmission line when the trunk slot line 31 is located on one side of the symmetry line 6 and connected to the slot line branch 31, θ4 is the electrical length of the connecting slot line 33 located on one side of the symmetry line 6, θ 2、 θ 3、 The sum of θ4 is the electrical length of the main slot line 32 on one side of the symmetry line 6, Z 4,even represents the characteristic impedance of the sub-resonator 4, θ6 represents the electrical length of the sub-resonator 4 on one side of the symmetry line 6, L1 is the equivalent inductance of the metal between the sub-resonator 4 and the main resonator 32 on the metal layer 12 and intersecting the symmetry line 6, and R1 is half of the resistance value of the resistor 5.

[0036] Figure 4 The measured results of the structure consisting of only the coupled microstrip line 1 and the main resonator 3 in the embodiment of the present invention are given. The results show that S dd21represents the differential mode transmission coefficient, S dd11 represents the differential mode reflection coefficient, S cc21 represents the common mode transmission coefficient, S cc11 represents the common mode reflection coefficient, S cd21 represents the transmission coefficient of the common mode response to differential mode excitation, S dd21 Represents the reflection coefficient of the common mode response to differential mode excitation. Common mode transmission coefficient S CC21 The common-mode rejection bandwidth of less than -10dB covers 2.28 GHz-6.45 GHz, with a relative bandwidth of 95.53%.

[0037] Figure 5 and Figure 6 The measured results of the mixed-mode scattering parameters of the overall structure of the embodiment of the present invention and the absorption rate curve varying with frequency are given, where S dd21 represents the differential mode transmission coefficient, S dd11 represents the differential mode reflection coefficient, S cc21 represents the common mode transmission coefficient, S cc11 represents the common mode reflection coefficient, S cd21 represents the transmission coefficient of the common mode response to differential mode excitation, S dd21 Represents the reflection coefficient of the common mode response of differential mode excitation. With the help of a hybrid resonant structure composed of two resonators, the common mode filter can achieve more than 10dB suppression of 1.56 GHz-6.26 GHz common mode noise, with a relative bandwidth of 120.2%, and has two absorption bands with an absorption rate of more than 80% at 1.32 GHz-2.86 GHz and 4.37 GHz-4.96 GHz. The common mode transmission coefficient S CC21 In addition to the suppression bandwidth of less than -10dB, there is an absorption band with an absorption rate of more than 60% at 7.37 GHz -9.81 GHz.

[0038] Figure 7 The measured data of the eye diagram of the differential mode signal transmitted at a rate of 10 Gbps are provided, and the results show that the embodiment of the present invention can ensure the normal transmission of the differential mode signal.

[0039] The performance of the common-mode filter is simulated in full-wave simulation software, and physical processing and testing are carried out to verify the correctness of the design of the present invention; the common-mode filter achieves ultra-wideband common-mode noise suppression and has multiple absorption bands, which greatly reduces electromagnetic interference and signal integrity degradation caused by common-mode noise, while not destroying the signal integrity of the differential mode signal.

[0040] The present invention can change the size of the main resonator 3 to adjust the position of the common mode suppression bandwidth, predict the absorption band position by calculating the input impedance of the equivalent circuit, and achieve flexible application by adjusting the length matching of the sub-resonator 4 and adjusting the absorption band position.

[0041] In manufacturing, the ultra-wideband common mode filter with dual absorption bands can be manufactured using a planar printed circuit board (PCB) process, can be manufactured using an integrated passive device (IPD) process, or can be manufactured using processes such as high temperature co-fired ceramic (HTCC) or low temperature co-fired ceramic (LTCC); in this embodiment, the RO4003C dielectric substrate of ROGERS Company is used to verify the correctness of the design.

[0042] According to the above, the present invention can be realized.

[0043] The above descriptions are merely embodiments of the present invention and are not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. within the design methods and principles of the present invention should be included in the protection scope of the present invention.

Claims

1. A multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure, characterized in that The filter comprises a coupled microstrip line (1), a dielectric substrate (2), a main resonator (3), a sub-resonator (4), and a resistor (5); the filter has an upper and lower surface, the coupled microstrip line (1) comprises a metal conductive strip (11) located above the dielectric substrate (2) and a metal ground layer (12) located below the dielectric substrate (2); one end of the coupled microstrip line (1) is connected to an input port (71), and the other end is connected to an output port (72); the main resonator (3) is etched in the middle of the metal ground layer (12); The sub-resonator (4) is etched on the outside of the main resonator (3) in the metal layer (12); the metal guide strip (11) is located in the main resonator (3); the coupling microstrip line (1) is coupled with the main resonator (3) and the sub-resonator (4) to realize hybrid resonance; the resistor (5) is located at the intersection of the sub-resonator (4) and the symmetry line (6), spanning the gap of the sub-resonator (4); and the two ends of the resistor (5) are respectively connected to the metal layer (12) inside the metal guide strip (11) and the metal layer (12) outside the metal guide strip (11).

2. A multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that The coupled microstrip line (1) is symmetrically distributed about the symmetry line (6), and the metal conductive strip (11) in the middle portion is a wave-like structure with multiple bends; changing the shape characteristics or length of the bends can adjust the common mode suppression frequency range and suppression degree.

3. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that The main resonator (3) comprises short-circuit slot line branches (31), a main slot line (32), and a connecting slot line (33), and is symmetrically distributed about a symmetry line (6); the short-circuit slot line branches (31) are sequentially arranged and distributed in a direction from an input port (71) to an output port (72), and are connected to the main slot line (32) of the main resonator (3); the connecting slot line (33) is located at the end of the main slot line (32) and on a side close to the output port (72), and is connected to the main slot lines (32) on both sides of the symmetry line (6); the common mode suppression frequency band and suppression strength can be adjusted by changing the number or spacing of the short-circuit slot line branches (31).

4. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that The sub-resonator (4) is symmetrically distributed about the symmetry line (6), the upper and lower sides of the sub-resonator (4) are a wave-like structure with multiple bends, and the upper and lower sides of the sub-resonator (4) are connected on one side of the input port (71); adjusting the length and shape characteristics of the sub-resonator (4) can adjust the common mode suppression degree and adjust the common mode transmission coefficient S CC21 The number of absorption bands within the common mode rejection bandwidth less than -10 dB, divided by the common mode transmission coefficient S CC21 In addition to the common-mode rejection bandwidth of less than -10dB, there are also absorption bands at higher frequencies.

5. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that The loaded resistor (5) is a main component for absorbing common mode noise, and its resistance value is equal to the common mode input impedance; the resistor (5) is a chip resistor, a ceramic resistor, a carbon film resistor or a chip resistor.

6. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that Changing the package size of the resistor (5) can adjust the parasitic effect and power capacity of the resistor.

7. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that The coupled microstrip line (1) serves as a transmission line for differential signals, and the differential mode and common mode characteristic impedances can be adjusted by changing the line width and line spacing of the metal conductive strip (11) in the coupled microstrip line (1).

8. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that In the coupled microstrip line (1), the wave-like structure with multiple bends is an arc, a 45° bend or a right angle.

9. The multi-absorption band ultra-wideband common mode filter based on a hybrid resonator structure according to claim 1, characterized in that In the sub-resonator (4), the wave-like structures with multiple bends on the upper and lower sides are arcs, circles or triangles.

Citation Information

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