CN113422591B - Multichannel filter based on quasi-periodic structure - Google Patents
Multichannel filter based on quasi-periodic structure Download PDFInfo
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- CN113422591B CN113422591B CN202110669468.XA CN202110669468A CN113422591B CN 113422591 B CN113422591 B CN 113422591B CN 202110669468 A CN202110669468 A CN 202110669468A CN 113422591 B CN113422591 B CN 113422591B
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Abstract
The invention discloses a multichannel filter based on a quasi-periodic structure, which is of a hollow tubular structure formed by coaxially arranging two kinds of circular rings with different diameters according to a quasi-periodic sequence, wherein the quasi-periodic sequence is a generalized fibonacci sequence. The band structure of the filter has a plurality of filtering channels and the channel width is uniform. The number and width of the filtering channels can be regulated and controlled by changing algebra and layer number of the generalized fibonacci sequence. And the working frequency range of the filter can be changed by changing the size of the waveguide structure in equal proportion. The filter based on the quasi-periodic structure has the band structure with a plurality of pass bands and the function of multi-channel filtering. And the number of the channels can be adjusted according to actual requirements. The method has the advantages of simple manufacturing process, good filtering effect, tunable channel number and the like, and has very wide application prospect in the fields of acoustic wave control, filters and the like.
Description
Technical Field
The invention relates to the technical field of multichannel filters, in particular to a multichannel filter based on a quasi-periodic structure.
Background
Acoustic wave control technology based on quasi-periodic structure is one of the emerging technologies in recent years, and the design and development of related functional devices are also attracting attention of researchers in various countries. Quasiperiodic structures have many excellent physical properties such as long-range symmetry, self-similarity, and topological properties. Therefore, the technology is used for manufacturing the multifunctional filter and has wide development prospect in the field of fluctuation control engineering.
Quasi-periodic is a structure that is intermediate between periodic and non-periodic. With the rapid development of artificial materials, quasi-periodic structures have become research hotspots in many fields such as condensed physics, materials science, crystallography and the like. The quasi-periodic structure is more complex than the periodic structure. Therefore, the guided wave mode, the band structure, and the sound field distribution in the quasi-periodic structure are also very complicated, and thus excellent physical properties that many periodic structures do not possess are brought about. Although quasiperiodic structures have unique physical properties and rich sound field structures, there are still certain difficulties in application and regulation. Therefore, the physical characteristics are effectively regulated, and a quasi-periodic structure with more functions and related functional devices can be developed.
In recent years, multichannel filters have been patented in many fields. In 2004, the one-dimensional photonic crystal multichannel filter was introduced in the patent filed by the university of henna technology, the main filter element of which is a photonic crystal film. The filter not only can meet the technical requirements of wavelength division multiplexing in a communication system, but also can expand the capacity of the communication system. In 2017, jiang Nada describes a tunable multichannel filter based on a silicon-based graphene bragg grating structure. The effective refractive index of the structure is periodically changed by regulating and controlling the applied voltage, so that the Bragg reflector is formed. Under the combined action of the grating structure and the applied voltage, a Fabry-Perot cavity is formed inside the filter, and the effect of multi-channel broadband filtering is realized by introducing a plurality of defects. In 2020, a design method of a multichannel filter is proposed by the nobis (Tianjin) microsystems, inc. The filter is composed of two large resonators, and each resonator is formed by cascading a plurality of resonance groups. However, the above-described multi-channel filters are designed based on periodic structures. Compared with a periodic structure, the arrangement of elements in the quasi-periodic structure is more flexible and various, and the quasi-periodic band structure is more abundant.
Disclosure of Invention
Aiming at the prior art, the technical problem to be solved by the invention is to provide a multi-channel filter based on a quasi-periodic structure, which has more filtering channels, the number of the filtering channels and the channel width are adjustable, and the filter based on the quasi-periodic structure has a band structure which not only has a plurality of pass bands and a multi-channel filtering function, but also has the number which can be adjusted according to actual requirements.
In order to solve the technical problems, the multichannel filter based on the quasi-periodic structure is a waveguide structure arranged according to a quasi-periodic sequence, and the waveguide structure is a hollow tubular structure formed by coaxially arranging two circular rings with different diameters according to the quasi-periodic sequence.
The invention also includes:
1. the quasi-periodic sequence is a generalized fibonacci sequence.
2. The arrangement rule of the generalized fibonacci sequence is specifically as follows: the ring with smaller diameter is A, the ring with larger diameter is B, and the lengths of A and B are equal; the recurrence relation of two circular arrangements of the k+1th generation structure satisfies:
S 1 ＝B m ，S 2 ＝B m A n or S 1 ＝A m ，S 2 ＝A m B n M and n are any two positive integers, < ->
A kth generation of structures S representing m successive arrangements of said filter structures k Then n serially arranged kth-1 th generation S are arranged k-1 Structure is as follows.
3. The algebra of the generalized fibonacci sequence is adjusted to regulate and control the width of a filtering channel of the filter: when the algebra of the generalized fibonacci sequence is increased, the width of the filtering channel is narrowed; the number of the filter channels can be regulated and controlled by adjusting m or n: when m or n is increased, the number of channels of the filter in the operating frequency range increases.
4. When m=n, the band characteristics of the multi-channel filter are that the pass band and the forbidden band are alternately arranged to form a plurality of channels, and the bandwidths of the filtering channels are equal.
5. The center frequency f of the working frequency band is adjusted by adjusting the size of the filter, specifically:
wherein v is the sound velocity in the air, d is the average straight of the rings A and BDiameter, k n Is the zero point of the zero order bessel function.
The invention has the beneficial effects that: the invention designs the filter with multiple channels by utilizing excellent physical characteristics of the quasi-periodic structure and rich band gap structures. The multichannel filter based on the quasi-periodic structure is a hollow tubular structure formed by coaxially arranging two circular rings with different diameters according to a quasi-periodic sequence. According to the quasi-periodic structure of the generalized fibonacci array, the band characteristics are that pass bands and forbidden bands are alternately arranged to form a plurality of channels, and the width of the filtering channels is uniform. The number of the filtering channels of the filter can be regulated and controlled by regulating algebra of the generalized fibonacci sequence and the number of layers. The operating frequency band of the filter can also be adjusted by scaling up or down equally. The invention has the beneficial effects that the filter is based on a quasi-periodic structure and has the function of multichannel filtering. Compared with the traditional filter based on the periodic structure, the filter based on the quasi-periodic structure has more filtering channels due to the rich band gap structure of the quasi-periodic structure. The number and the width of the filtering channels of the filter can be regulated and controlled by controlling algebra and layer number of the generalized fibonacci sequence, so that the filter has a multi-channel tunable filtering function. The hollow tubular filter can ensure good filtering effect while not obstructing air flow. Besides, the hollow structure has simple manufacturing process, greatly reduces the material cost for manufacturing the filter, and has very wide application prospect in the fields of acoustic wave control, filters and the like.
Drawings
Fig. 1 is a schematic diagram of a multi-channel filter based on a quasi-periodic structure. The hollow tubular structure is formed by coaxially arranging two circular rings with different diameters according to a quasi-periodic sequence. The smaller diameter ring is labeled a and the larger diameter ring is labeled B. Diameter d of the rings A and B respectively A And d B . The lengths of A and B are equal to L.
Fig. 2 is a transmission spectrum of a third generation generalized fibonacci sequence layer number 3 quasi-periodic filter.
Fig. 3 shows the number of filter channels and the filter frequency range of the filter as a function of the number of layers of the third generation generalized fibonacci sequence.
Detailed Description
The invention is further described below with reference to the drawings and the detailed description.
The multichannel filter based on the quasi-periodic structure is a waveguide structure with an internal structure arranged according to a quasi-periodic sequence. The band structure has the characteristic that a plurality of pass bands and forbidden bands are alternately distributed. The quasi-periodic structure waveguide structure is a hollow tubular structure formed by coaxially arranging two kinds of circular rings with different diameters according to a quasi-periodic sequence. The quasi-periodic sequence according to which the internal structures of the waveguide are arranged is a generalized fibonacci sequence. The band structure of the filter has a plurality of filtering channels and the channel width is uniform. The number of layers and algebra of the generalized fibonacci sequence can be adjusted to regulate the number of filtering channels and the width of the filtering channels of the filter. The wall of the quasi-periodic structured waveguide has a certain thickness, typically not less than 4 mm. The pipe wall material is generally made of a material with high acoustic impedance, such as stainless steel, polyethylene resin, concrete and the like. Changing the dimensions of the waveguide structure in equal proportions can change the operating frequency range of the filter.
In the schematic diagram of the filter based on the quasi-periodic structure of fig. 1, the quasi-periodic structure is a hollow tubular structure formed by coaxially arranging two kinds of circular rings with different diameters according to a quasi-periodic sequence. The basic units forming the quasi-periodic structure are a ring A with a smaller diameter and a ring B with a larger diameter. Diameter d of A A Diameter d with B B 55mm and 85mm respectively. A and B have lengths equal to 175mm and are denoted as L. The operating frequency f of the filter can be adjusted according to the following formula:
wherein v is the sound velocity in the air, d is the average diameter of the rings A and B, k n Zero as a zero-order bessel function, k when n=0, 1,2, … n ＝0，3.8317，7.0156…。
The unit arrangement in the quasi-periodic structure satisfies the generalized fibonacci sequence, and the recurrence relation is as follows:
then the quasi-periodic structure is arranged according to a recurrence relation:
Here, m and n are any two positive integers. The number of channels of the filter can be designed according to the actual filtering requirements as long as the recursive relation of the generalized fibonacci sequence is satisfied. In order to ensure that the bandwidths of the filtering channels are equal and thus a good filtering effect is achieved, m and n should be ensured to be equal, in which case we call m or n the number of layers of the generalized fibonacci sequence. For example, when m=n=3 (number of layers is 3), the third generation structure of the generalized fibonacci sequence is arranged as S 3 =bbbaaabbbaaabbbaaabbbbbbbbb. When m and n are selected to be unequal, the number of channels of the filter in the operating frequency range is increased, but the bandwidth of the filtering channels becomes uneven. When the algebra of the generalized fibonacci sequence is increased, the number of the filtering channels is unchanged, and the width of the filtering channels is slightly narrowed, so that the width of the filtering channels can be finely adjusted by adjusting the algebra of the generalized fibonacci sequence.
The transmission spectrum of the quasiperiodic structure based filter shown in fig. 1 at a frequency window of 0-1000Hz is plotted in fig. 2. As shown, three channels with high filtering effect occur in the frequency window of 0-1000 Hz. The frequency ranges of the three filtering channels are respectively: 69-254Hz,392-576Hz and 715-898Hz. The widths of the three filter channels are 185Hz, 184Hz and 183Hz, respectively. The channel widths differ very uniformly by no more than 2Hz.
The number of filtering channels and the variation of the filtering frequency range from the number of filter layers based on the quasi-periodic structure are shown in fig. 3. The number of the filtering channels is consistent with the number of layers of the third generation generalized fibonacci sequence, and the frequency width of the filtering channels is uniform. The black area in the figure shows the filter frequency range of the filter channel. Also taking the third generation generalized fibonacci sequence as an example, the filter frequency range of the filter channel is enumerated as the number of layers of the quasi-periodic structure increases from 2 to 7. It is obvious from the figure that the number of the filtering channels is equal to the number of layers of the third generation generalized fibonacci sequence, and the frequency width of the filtering channels is equal. Therefore, according to the actual filtering requirement, the number of the filtering channels and the filtering frequency range of the filter are regulated and controlled by a method of adjusting the layer number of the quasi-periodic structure, so that the function of multi-channel tunable filtering is realized.
Claims (1)
1. A multi-channel filter based on a quasi-periodic structure, characterized in that: the waveguide structure is arranged according to a quasi-periodic sequence, the quasi-periodic sequence is a generalized fibonacci sequence, and the waveguide structure is a hollow tubular structure formed by coaxially arranging two circular rings with different diameters according to the quasi-periodic sequence; the arrangement rule of the generalized fibonacci sequence is specifically as follows: the ring with smaller diameter is A, the ring with larger diameter is B, and the lengths of A and B are equal and L; the recurrence relation of two circular arrangements of the k+1th generation structure satisfies:
S 1 ＝B m ，S 2 ＝B m A n or S 1 ＝A m ，S 2 ＝A m B n M and n are any two positive integers, < ->
A kth generation of structures S representing m successive arrangements of said filter structures k Then n serially arranged kth-1 th generation S are arranged k-1 A structure; the algebra of the generalized fibonacci sequence is adjusted to regulate and control the width of a filtering channel of the filter: when generalized fibonacci is addedWhen algebra of the sequence is performed, the width of the filtering channel is narrowed; the number of the filter channels can be regulated and controlled by adjusting m or n: when m or n is increased, the number of channels of the filter in the working frequency range is increased; when m=n, the band characteristics of the multi-channel filter are that pass bands and forbidden bands are alternately arranged to form a plurality of channels, and the bandwidths of the filtering channels are equal; the center frequency f of the working frequency band is adjusted by adjusting the size of the filter, specifically:
wherein v is the sound velocity in the air, d is the average diameter of the rings A and B, k n Is the zero point of the zero order bessel function.
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| US6775448B2 (en) * | 2002-11-05 | 2004-08-10 | Mesophotonics Limited | Optical device |
| CN100444461C (en) * | 2006-09-22 | 2008-12-17 | 东南大学 | Base-plate integrative waveguide pseudo inductive through-hole filter |
| CN104007509A (en) * | 2014-05-16 | 2014-08-27 | 河南科技大学 | One-dimensional photonic crystal multi-channel filter and manufacturing method thereof |
| CN105842785A (en) * | 2016-05-20 | 2016-08-10 | 燕山大学 | Multichannel filter based on chirp porous silicon photonic crystal |
| CN107390306A (en) * | 2017-08-10 | 2017-11-24 | 江南大学 | Based on the tunable multi-channel filter of silicon substrate graphene Bragg-grating structure |
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| CN111490543A (en) * | 2020-03-13 | 2020-08-04 | 国网江苏省电力有限公司盐城供电分公司 | Fibonacci method-based virtual harmonic resistance type active filter control method |
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| Ting Liu 等.Interface States in the Acoustic Quasiperiodic System Based on Non-Bragg Resonances.《physica status solidi b 2021》.2021,第1-7页. * |
| 曹永军 ; 杨旭 ; .广义Fibonacci准周期结构声子晶体透射性质的研究.物理学报.2008,(第06期),第3620-3624页. * |
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