A filter
By setting up an integrated bending structure resonator in the filter frame and using the coupling opening on the partition wall to achieve cross-coupling, the existing filters have complex processes and high sensitivity in miniaturized design, and the effects of smaller, flexible design and cost reduction are achieved.
Patent Information
- Application Number
- CN201910043685.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2019-01-17
- Publication Date
- 2025-05-30
- Estimated Expiration
- 2039-01-17
AI Technical Summary
When existing filters meet the design requirements of micro-volume, it is difficult to achieve miniaturization. At the same time, the process is complex and sensitive, resulting in increased production costs and reduced production capacity.
The structure and processing process are simplified by providing a resonator with a plurality of bent structures in the filter frame, and cross-coupling between non-adjacent resonators is achieved by using the coupling openings on the partition wall.
The filter is reduced while reducing assembly labor costs, accumulated tolerances and contact losses, improving design flexibility and PIM performance, and reducing production costs.
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Figure CN111446529B_ABST
Abstract
Description
Technical Field
[0001] The present invention relates to a filter, and particularly to a filter with a more miniaturized volume. Background Art
[0002] With the rapid development of communication technologies, the requirements for the volume of filters are becoming increasingly stringent. It is often necessary to design resonators and suppress zeros in a limited tiny space to meet the requirements of in-band and out-of-band insertion loss suppression. However, several traditional filters can hardly meet the design requirements under such a tiny volume.
[0003] For example, in the patent with the application number: CN201710149229.5, a filter in the form of a frame structure is disclosed. In this solution, both sides of the mouth-shaped frame are open structures, and the partition wall divides the interior of the frame into two spaces. Perpendicular to this partition wall, there is a one-piece resonator. The resonator is bent into an L shape or a T shape to reduce the space requirements. However, such a form still has limitations on the miniaturized volume of the filter and is difficult to meet the design requirements of the tiny volume of the filter.
[0004] Moreover, the structure in which the above-mentioned resonator is bent into an L shape or a T shape also has limitations on the coupling method between resonators. Specifically, in the two spaces divided by the partition wall, the signal path is transmitted in a U-shaped form. In order to achieve cross-coupling in the U-shaped transmission path, conductors need to be added to two non-adjacent resonators. At this time, in order to achieve capacitive cross-coupling, the resonator and the conductor need to be fixed in an open-circuit form. For this purpose, the conductor is first fixed to the insulator, and then this fitting is fixed to the housing. If inductive cross-coupling is to be achieved, the conductor is fixed in a short-circuit form between two non-adjacent resonators. At this time, the conductor in the short-circuit form is fixed to the resonator by welding, and the used conductor is bent with a specific size and then combined with the resonator.
[0005] However, in order to form cross-coupling as described above, the structure of adding sheet-like or wire-like conductors in an open-circuit or short-circuit form between non-adjacent resonators requires adding insulators to the frame fixation or welding conductors in the form of wires to the resonators. Such structures will generate processing costs and processing tolerances, and the cross-coupling strength becomes very sensitive due to factors such as position tolerance and spacing when directly welding or using other forms to fix the sheet-like conductors to the resonators. Therefore, the complex process and increased sensitivity lead to an increase in manufacturing costs and a decrease in production capacity.
[0006] In addition, in order to ensure the transmission coupling between resonators, the arrangement direction of the resonators is restricted. Generally, the signal transmission path can only be in a straight line or U shape, so the positions of the input and output ports are also immutable, resulting in the inability to meet the diverse system requirements. Moreover, additional structural components need to be added to change the port positions. Summary of the Invention
[0007] The object of the present invention is to overcome the defects of the prior art and provide a filter with a more miniaturized volume.
[0008] To achieve the above object, the present invention proposes the following technical solution: A filter, comprising:
[0009] A filter frame, in which an accommodation space is formed;
[0010] At least two resonators disposed in the accommodation space and distributed along a signal transmission path, and adjacent two of the resonators on the signal transmission path are coupled and connected. Each resonator includes a main body portion and a bent portion. One end of the main body portion is integrally formed and grounded with the inner wall of the filter frame. The bent portion includes a first bent portion and a last bent portion, and the first bent portion and the last bent portion are connected to form a resonator structure spiraling in a counterclockwise or clockwise direction, or the bent portion includes a first bent portion, at least one intermediate bent portion and a last bent portion, and the intermediate bent portion connects the first bent portion and the last bent portion to form a resonator structure spiraling in a counterclockwise or clockwise direction.
[0011] Preferably, the first bent portion is bent from the other end of the main body portion in one direction or two directions.
[0012] Preferably, at least one partition wall is further disposed in the filter. A coupling gap is formed between the partition wall and the inner wall of the filter frame and is integrally formed with the filter frame. The partition wall divides the accommodation space into a plurality of accommodation chambers. The main body portion of the resonator is integrally formed and grounded with the partition wall, and / or integrally formed and grounded with the inner wall of the filter frame.
[0013] Preferably, the signal transmission path in the filter is transmitted in a U shape or an S shape according to the partition wall.
[0014] Preferably, one partition wall is disposed in the filter, and the partition wall is integrally formed in the middle of the filter frame. The signal transmission path in the filter is transmitted in a U shape according to the partition wall.
[0015] Preferably, a plurality of partition walls are disposed in the filter at intervals, and adjacent two partition walls respectively form coupling gaps with opposite two inner walls of the filter frame. The signal transmission path in the filter is transmitted in an S shape according to the partition wall.
[0016] Preferably, coupling openings are provided on the partition wall, and adjacent two resonators in different accommodation chambers are coupled and connected through the coupling openings to form cross-coupling.
[0017] Preferably, the main body portions of adjacent two resonators in different accommodation chambers are directly connected together through the coupling openings to achieve inductive cross-coupling.
[0018] Preferably, the bent portions of two adjacent resonators in different accommodation chambers are capacitively cross-coupled through coupling openings at an interval.
[0019] Preferably, the filter further includes an upper cover plate disposed at the upper end of the filter frame and a lower cover plate disposed at the lower end of the filter frame. The upper and lower cover plates enclose the accommodation space. In the direction perpendicular to the upper and lower cover plates, the thickness of the bent portion of the resonator is greater than the thickness of the main body portion.
[0020] Preferably, the filter further includes a signal input port and a signal output port that are disposed outside the filter frame and communicate with the accommodation space, and the signal input port and the signal output port are respectively located at two ends of the signal transmission path.
[0021] Preferably, the upper and lower cover plates are respectively assembled to the upper and lower ends of the filter frame by means of screw fixation, soldering or laser welding.
[0022] The beneficial effects of the present invention are as follows:
[0023] 1. By providing a resonator integrally formed with multiple bends (at least two bent portions) in the filter frame, it has a significant effect on the miniaturization of the filter. Moreover, the resonator and the frame are of an integral structure, reducing the assembly man-hour cost, reducing the cumulative tolerance and assembly tolerance, reducing the contact loss, and at the same time enabling the filter to have good PIM (Passive Inter-Modulation) performance.
[0024] 2. The shape of each resonator can be changed and designed as needed, and the coupling method between the resonators can be freely designed according to the shape of the resonator. In addition, the signal transmission path can be freely changed in combination with the partition wall, and the free change of the transmission path can further freely select the design position of the signal input / output port, improving the overall design flexibility of the filter.
[0025] 3. By using the opening part of the partition wall, the cross-coupling between non-adjacent resonators can be achieved without adding structural parts, so the processing and assembly tolerances caused by structural parts can be reduced, the processing difficulty of the product can be reduced, and the processing and assembly costs can also be greatly reduced. BRIEF DESCRIPTION OF THE DRAWINGS
[0026] Figure 1 is a three-dimensional structural schematic diagram of Embodiment 1 of the present invention;
[0027] Figure 2 is a top-view structural schematic diagram of Embodiment 1 of the present invention;
[0028] Figure 3It is a schematic diagram of the principle of the signal transmission path in Embodiment 1 of the present invention;
[0029] Figure 4 It is a schematic structural diagram of the resonator of the present invention;
[0030] Figure 5 It is a schematic diagram of the principle of the equivalent circuit in Embodiment 1 of the present invention;
[0031] Figure 6 It is a schematic diagram of the corresponding electrical performance curve in Embodiment 1 of the present invention;
[0032] Figure 7 It is a three-dimensional structural diagram of Embodiment 2 of the present invention
[0033] Figure 8 It is a three-dimensional structural diagram of Embodiment 3 of the present invention;
[0034] Figure 9 It is a top view structural diagram of Embodiment 3 of the present invention.
[0035] Reference numerals:
[0036] 1. Filter frame, 11. Accommodating space, 111. Accommodating chamber, 2 / 21 - 26. Resonator, 211. Main body part, 212. First bending part, 213. Last bending part, 214. Intermediate bending part, 3. Upper cover plate, 4. Adjustable structure, 5. Partition wall, 51. Coupling opening, 6. Coupling gap, 7. Signal input port, 8. Signal output port. Detailed implementation manners
[0037] Next, the technical solutions of the embodiments of the present invention will be clearly and completely described in conjunction with the drawings of the present invention.
[0038] A filter disclosed by the present invention realizes miniaturization of the filter volume by arranging a resonator with a plurality of bending structures integrally formed in the filter frame, and at the same time realizes diversification of the coupling mode between resonators, the signal transmission path, the signal port position, etc., improving the flexibility of filter design; and realizes cross-coupling between non-adjacent resonators by means of an opening on the partition wall, simplifying the structure and processing process of the filter.
[0039] Combined with Figures 1 to 3As shown in the figure, a filter disclosed by the present invention includes a filter frame 1 and at least two resonators 2. Among them, the upper and lower ends of the filter frame 1 are open. Of course, it can also be replaced by only the upper end being open. A hollow accommodation space 11 for accommodating the resonators is formed inside the filter frame 1. The openings on the upper and lower surfaces of the filter frame 1 can be respectively encapsulated by an upper cover plate 3 and a lower cover plate (not shown in the figure) to form a sealed accommodation space 11 inside; when only the upper end is open, only the upper cover plate 3 is used for encapsulation. During implementation, the upper and lower cover plates can be fixed by screws or assembled by soldering or laser welding. In addition, an adjustable structure 4 for adjusting the frequency and / or coupling amount can be added to the upper cover plate 3. During implementation, the adjustable structure 4 can include the cooperation of a screw and a nut, or can also adopt other forms such as extending a conductor through the cover plate surface. Moreover, the upper and lower cover plates can also be replaced by a PCB board.
[0040] A plurality of resonators 2 are arranged in the accommodation space 11 and are integrally formed with the filter frame 1. The resonators 2 can form various signal transmission paths in the accommodation space 11, such as a straight shape, a U shape, or an S shape. When forming a straight signal transmission path, a plurality of resonators 2 are arranged in the same row in the accommodation space 11 and are distributed from one side wall of the filter frame 1 to the opposite side wall, and the formed signal transmission path is a straight shape. And the plane where the resonators 2 are located is parallel or approximately parallel to the upper and lower surfaces of the filter frame 1, that is, horizontally arranged inside the filter frame 1.
[0041] As an alternative, at least one partition wall 5 integrally formed with the filter frame 1 can also be provided inside the filter frame 1. Combining Figures 1 to 3 As shown in the figure, the partition wall 5 divides the accommodation space 11 into a plurality of accommodation chambers 111. At least two of the resonators 2 are arranged in each accommodation chamber 111, and the distribution of the resonators 2 in each accommodation chamber 111 is the same as or similar to the distribution method of the above-mentioned resonators 2 arranged in a straight shape. For reference, see the above description and details are not repeated here. In this way, the signal transmission paths formed by the filters 2 in the plurality of accommodation chambers 111 can be a U shape, an S shape, or others.
[0042] The partition wall 5 is arranged between two adjacent accommodation chambers 111 and is used to isolate the resonators 2 in different accommodation chambers 111. The partition wall 5 is integrally formed with the filter frame 1. In this embodiment 1, the partition wall 5 is located in the middle of the filter frame 1 and divides the accommodation space 11 into two accommodation chambers 111. A plurality of resonators 2 are arranged in each accommodation chamber 111 (as Figure 2 and Figure 3 shown, resonators 21 to 23 are arranged in the upper accommodation chamber, and resonators 24 to 26 are arranged in the lower accommodation chamber). The partition wall 5 does not contact the right side wall of the filter frame 1, and a coupling gap 6 is formed therebetween, as Figure 1As shown, the coupling gap 6 enables adjacent two resonators (i.e., resonators 23 and 24) located in different accommodation chambers to generate coupling. The partition wall 5 forms a signal transmission path between the resonators 21-26. In the first embodiment, the signal transmission path is U-shaped. That is to say, the signal transmission path can be freely designed according to the setting position and the number of partition walls 5, etc.
[0043] As Figure 4 shown, each resonator 2 specifically includes a main body portion 211 and a bent portion. Among them, one end of the main body portion 211 is grounded. When the partition wall 5 is not provided in the filter frame 1, this grounded end can be integrally formed with any side wall of the filter frame 1 as needed, such as being integrally formed with the rear side wall of the filter frame 1, and the other end extends towards the front side wall of the filter frame 1. Also, it can be integrally formed with the left side wall of the filter frame 1, and the other end extends towards the right side wall of the filter frame 1. When the partition wall 5 is provided, this grounded end can be integrally formed with the partition wall 5 as needed, and / or integrally formed with any side wall of the filter frame 1. As Figures 1 to 3 shown, in the first embodiment, the grounded ends of the filters 21, 22, 25, and 26 are all integrally formed with the partition wall 5, while the grounded ends of the filters 23 and 24 are integrally formed with the right side wall of the filter frame 1. That is to say, the grounded end of the main body portion 211 can be freely changed in design up, down, left, and right within the filter frame 1.
[0044] The bent portion is connected to the other end of the main body portion 211 and is bent to form. The bent shape of the bent portion can be freely changed in design according to actual needs and is not limited here. That is to say, the shape of the resonator 2 can be bent to form various designs according to needs. Specifically, as Figure 4 shown, the bent portion includes a first bent portion 212 and a last bent portion 213. Among them, the first bent portion 212 is bent from the other end of the main body portion 211 in one direction or two directions; the first bent portion 212 and the last bent portion 213 are connected to form a resonator structure that spirals in a counterclockwise or clockwise direction. Or, as an alternative, in addition to the first bent portion 212 and the last bent portion 213, the bent portion may further include at least one intermediate bent portion 214. Among them, the first bent portion 212 is bent from the other end of the main body portion 211 in one direction or two directions, and the intermediate bent portion 214 connects the first bent portion 212 and the last bent portion 213 to form a resonator structure that spirals in a counterclockwise or clockwise direction.
[0045] As Figure 4As shown, in this Embodiment 1, the bent portion is connected to the other end of the main body portion 211 to form at least three bends by vertically bending in the clockwise or counterclockwise direction. That is, the bent portion includes a first bent portion 212, an intermediate bent portion 214, and a last bent portion 213. Among them, the first bent portion 212 is connected to the other end of the main body portion 211 to form a vertical bend. The intermediate bent portion is connected to the end of the first bent portion 212 to form a vertical bend. The last bent portion 213 is connected to the end of the intermediate bent portion 214 to form a vertical bend. Compared with the existing L-shaped and T-shaped resonators, the resonator structure designed by the present invention can achieve a more miniaturized filter, and the frequency of the filter is lower. Preferably, in the direction perpendicular to the upper and lower ends of the filter frame, the bent portion is thickened, that is, the thickness of the bent portion is greater than the thickness of the main body portion 211, so that the volume of the resonator can be further reduced under the requirement of the same frequency.
[0046] Electromagnetic hybrid coupling occurs between two adjacent resonators 2 on the signal transmission path. Specifically, the main coupling method is determined by the shape and arrangement position of the resonator 2. The coupling amount between the resonators 2 can be adjusted by the coupling area and spacing between the resonators 2. It should be noted that the coupling of a general TEM mode filter is the coexistence of electrical coupling (i.e., capacitive coupling) and magnetic coupling (i.e., inductive coupling). The one with a larger coupling amount in these two couplings is called the dominant coupling, and the dominant coupling mode in the filter of the present invention can be freely selected by the shape of the resonator 2. For example, in the integrated 6th-order filter in this Embodiment 1, the formed signal transmission path is the U-shaped path formed by the resonators 21 to 26.
[0047] Preferably, at least one group of two adjacent resonators in different accommodation chambers are coupled and connected to achieve cross-coupling. As Figures 1 to 3 shown, cross-coupling transmission paths are formed between two adjacent resonators in different accommodation chambers through the correspondingly added coupling openings 51 on the partition wall 5. The coupling amount of the cross-coupling is adjusted according to the area of the coupling opening 51, and / or the shape of the resonators coupled through the coupling opening 51 and the coupling spacing. And the selection of the cross-coupling mode is determined according to the dominant coupling mode. In this Embodiment 1, a coupling opening 51 is provided at the position corresponding to the resonators 22 and 25 on the partition wall 5. The main body portions 211 of the resonator 22 and the resonator 25 are directly connected together through this coupling opening 51 to achieve inductive cross-coupling, that is, inductive cross-coupling is increased, forming 2 transmission zeros; and a coupling opening 51 is also provided at the position corresponding to the resonators 21 and 26 on the partition wall 5, so that the bent portions of the resonators 21 and 26 are spaced apart by a certain distance, and capacitive coupling is formed through this coupling opening 51, that is, capacitive cross-coupling is increased. In this embodiment, two zeros with opposite phases are generated in the high-frequency band and the low-frequency band of the passband through one cross-coupling. Therefore, a total of 4 transmission zeros are generated by the two cross-couplings. As Figure 5In the schematic diagram shown, the cross-coupling between resonators 22 and 25 is inductive coupling, and the cross-coupling between resonators 21 and 26 is capacitive coupling. As Figure 6 shown in the corresponding electrical performance curve, through the inductive cross-coupling and capacitive cross-coupling formed by two coupling openings 51, a total of 4 zeros are formed, so a high-performance filter with good attenuation characteristics can be realized. The strength and position of each zero can be independently controlled.
[0048] Furthermore, as Figures 1 to 3 shown, the filter further includes a signal input port 7 and a signal output port 8. These two ports 7 and 8 are respectively arranged at the two ends of the above signal transmission path. The positions of the signal input and output ports 7 and 8 are determined according to the direction of the signal transmission path. That is to say, according to the different signal transmission paths, their installation positions can also be correspondingly different. Therefore, changing the signal transmission path can change the positions of the signal input and output interfaces 7 and 8. From the above description, it can be seen that the signal transmission path can be freely designed by the installation position of the partition wall 5. In Embodiment 1, the signal input port 7 is arranged at a position outside the filter frame 1 close to the resonator 21, and the signal output port 8 is arranged at a position outside the filter frame 1 close to the resonator 26. During implementation, the signal input port 7 and the signal output port 8 can also have various forms. In this embodiment, the signal input and output ports 7 and 8 are in the form of inner cores, and can also be changed to connectors, or combined with a PCB board (i.e., the upper cover plate and the lower cover plate) at the upper end and the lower end to form the signal input and output ports 7 and 8.
[0049] Again, as Figure 7 shown, there are 8 integrated resonators 2 in a filter frame 1, forming a 4-cavity band-pass filter. Among them, 3 partition walls 5 arranged in the same row (such as distributed from the left side wall of the filter frame 1 to the right side wall of the filter frame 1) are arranged in the filter frame 1. The 3 partition walls 5 divide the accommodation space 11 into 4 accommodation chambers 111. Two resonators 2 are arranged in each accommodation chamber 111. The shape, grounding position, etc. of the resonators 2 refer to the description of Embodiment 1 above and will not be elaborated here. And according to the shape of the resonators 2 and the position of mutual coupling, the dominant coupling mode between the resonators 2 in Embodiment 2 is controlled to be an electric coupling mode or a magnetic coupling mode.
[0050] The two coupling gaps 6 between two adjacent partition walls 5 are located on different sides, so that the signal transmission path in the filter 2 is transmitted in an S shape according to the partition wall 5. According to this S-shaped signal transmission path, the positions of the signal input and output ports 7 and 8 can be controlled. The signal input and output ports 7 and 8 are respectively at the two ends of the signal transmission path, and the direction of the signal transmission path determines the positions of the signal input and output ports 7 and 8. Of course, the signal transmission path of the resonators in Embodiment 2 can also be U-shaped, as Figure 8 、 9As shown, a partition wall 5 is provided in the middle of the filter frame 1.
[0051] That is to say, the shape and grounding position of the resonator 2 of the present invention can be freely designed, and the dominant coupling mode between the resonators 2 can be determined by the coupling positions of the coupled resonators 2, so it can also be freely designed; in addition, the setting position of the partition wall 5 can be freely designed, and the signal transmission path is determined by the setting position of the partition wall 5, so it can also be freely designed. Moreover, the signal input and output ports 7 and 8 are determined by the signal transmission path, so they can also be freely designed; further, the cross-coupling between the resonators 2 is determined according to the performance requirements of the filter, so it can also be freely designed. In the present invention, the design of the shape of the resonator 2, the coupling mode between the resonators 2, the signal transmission path, the signal input and output ports 7 and 8, and the cross-coupling mode of the filter can be freely designed according to needs, and are not limited to those described in the above three embodiments.
[0052] From Figure 1 , Figure 7 and Figure 8 it can be seen that except for the connectors, the present invention has no additional assembly structural parts, and the processing and assembly costs can be greatly reduced. And when cross-coupling is formed between non-adjacent resonators, there are no additional structural parts, and cross-coupling can be achieved only by opening holes in the partition wall. Therefore, the processing and assembly tolerances caused by the structural parts can be reduced, and the difficulty of the product is reduced.
[0053] The technical content and technical features of the present invention have been disclosed as above. However, those skilled in the art may still make various substitutions and modifications that do not depart from the spirit of the present invention based on the teachings and disclosures of the present invention. Therefore, the protection scope of the present invention should not be limited to the content disclosed in the embodiments, but should include various substitutions and modifications that do not depart from the present invention and are covered by the claims of this patent application.
Claims
1. A filter, characterized in that, comprising: a filter frame, in which an accommodation space is formed; at least two resonators disposed in the accommodation space and distributed along a signal transmission path, adjacent two of the resonators on the signal transmission path are coupled and connected, each resonator includes a main body portion and a bent portion, one end of the main body portion is integrally formed and grounded with the filter frame, the bent portion is connected to the other end of the main body portion and is bent to form, the bent portion includes a first bent portion and a last bent portion, the first bent portion and the last bent portion are connected to form a resonator structure spiraling in one of the counterclockwise and clockwise directions, or the bent portion includes a first bent portion, at least one intermediate bent portion and a last bent portion, and the intermediate bent portion connects the first bent portion and the last bent portion to form a resonator structure spiraling in one of the counterclockwise and clockwise directions, wherein the counterclockwise and clockwise directions are relative to the plane where the signal transmission path is located, and electromagnetic hybrid coupling occurs between adjacent two resonators on the signal transmission path.
2. The filter according to claim 1, characterized in that, the first bent portion is bent from the other end of the main body portion in one or two directions.
3. The filter according to claim 1, characterized in that, at least one partition wall is further disposed in the filter, a coupling gap is formed between the partition wall and the inner wall of the filter frame and is integrally formed with the filter frame, the partition wall divides the accommodation space into a plurality of accommodation chambers, the main body portion of the resonator is integrally formed and grounded with the partition wall, and / or is integrally formed and grounded with the inner wall of the filter frame.
4. The filter according to claim 3, characterized in that, the signal transmission path in the filter is transmitted in a U shape or an S shape according to the partition wall.
5. The filter according to claim 3, characterized in that, one partition wall is disposed in the filter, the partition wall is integrally formed in the middle of the filter frame, and the signal transmission path in the filter is transmitted in a U shape according to the partition wall.
6. The filter according to claim 3, characterized in that, a plurality of partition walls are disposed in the filter at intervals, and adjacent two partition walls respectively form coupling gaps with opposite two inner walls of the filter frame, and the signal transmission path in the filter is transmitted in an S shape according to the partition walls.
7. The filter according to any one of claims 3 to 6, characterized in that, coupling openings are provided on the partition wall, and adjacent two resonators in different accommodation chambers are coupled and connected through the coupling openings to form cross-coupling.
8. The filter according to claim 7, characterized in that, the main body portions of adjacent two resonators in different accommodation chambers are directly connected together through the coupling openings to realize inductive cross-coupling.
9. The filter according to claim 7, characterized in that, the bent portions of adjacent two resonators in different accommodation chambers are capacitively cross-coupled through the coupling openings at an interval.
10. The filter according to claim 1, characterized in that, The filter further includes an upper cover plate disposed at the upper end of the filter frame and a lower cover plate disposed at the lower end of the filter frame. The upper and lower cover plates enclose the accommodation space. In a direction perpendicular to the upper and lower cover plates, the thickness of the resonator bending portion is greater than the thickness of the main body portion.
Citation Information
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