CN113422591B - Multichannel filter based on quasi-periodic structure - Google Patents

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

A Multi-Channel Filter Based on Quasi-Periodic Structure

technical field

The invention relates to the technical field of multi-channel filters, in particular to a multi-channel filter based on a quasi-periodic structure.

Background technique

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 have also attracted the attention of researchers from various countries. Quasi-periodic structures have many excellent physical properties, such as long-range symmetry, self-similarity, and topological properties. Therefore, this kind of technology is used in the manufacture of multifunctional filters, and has broad development prospects in the field of wave control engineering.

Quasi-periodic is a structure between periodic and non-periodic. With the rapid development of artificial materials, quasi-periodic structures have become a research hotspot in many fields such as condensed matter physics, materials science, and crystallography. Compared with periodic structures, quasi-periodic structures are more complicated. Therefore, the guided wave mode, band structure and sound field distribution in the quasi-periodic structure are also very complicated, and thus bring many excellent physical properties that the periodic structure does not have. Although the quasi-periodic structure has unique physical properties and rich sound field structure, it still has certain difficulties in application and regulation. Therefore, by effectively controlling these physical properties, quasi-periodic structures and related functional devices with more functions can be developed.

In recent years, multi-channel filters have been patented in many fields. In 2004, Henan University of Science and Technology introduced a one-dimensional photonic crystal multi-channel filter in the patent application, and its main filter element is a photonic crystal film. The filter can not only meet the technical requirements of wavelength division multiplexing in the communication system, but also can expand the capacity of the communication system. In 2017, Jiangnan University described a tunable multi-channel filter based on a silicon-based graphene Bragg grating structure in a patent application. By adjusting the applied voltage, the effective refractive index of the structure is periodically changed, thereby forming a Bragg reflector. Under the joint action of this 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 multiple defects. In 2020, North (Tianjin) Microsystems Co., Ltd. proposed a design method for multi-channel filters. The filter is composed of two resonators, and each resonator is formed by cascading multiple resonant groups. However, the above multi-channel filters are all designed based on periodic structures. Compared with the periodic structure, the arrangement of elements in the quasi-periodic structure is more flexible and diverse, and the quasi-periodic band structure is more abundant.

Contents of the invention

In view of the above-mentioned prior art, the technical problem to be solved by the present invention is to provide a multi-channel filter based on a quasi-periodic structure with more filtering channels, the number of filtering channels and adjustable channel width. The filter, its spectral band structure not only has multiple passbands, but also has the function of multi-channel filtering, and the number of these channels can be adjusted according to actual needs.

In order to solve the above technical problems, a multi-channel filter based on a quasi-periodic structure of the present invention is a waveguide structure arranged in a quasi-periodic sequence. A hollow tubular structure arranged coaxially.

The present invention also includes:

1. The quasi-periodic sequence is a generalized Fibonacci sequence.

S₁＝B^m，S₂＝B^mAⁿ或者S₁＝A^m，S₂＝A^mBⁿ，m和n为任意两个正整数，/>

代表所述滤波器结构为m个连续排列的第k代结构S_k后再排列n个连续排列的第k-1代S_k-1结构。2. The arrangement rules of the generalized Fibonacci sequence are as follows: among the two rings with different diameters, the ring with the smaller diameter is A, and the ring with the larger diameter is B, and the lengths of A and B are equal; The recurrence relation of the two ring arrangements of the first-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, />

It means that the filter structure is m consecutively arranged k-th generation structures S _k , and then n consecutively arranged k-1th generation S _k-1 structures are arranged.

3. Adjusting the algebra of the generalized Fibonacci sequence can control the filter channel width of the filter: when increasing the algebra of the generalized Fibonacci sequence, the width of the filter channel becomes narrower; adjusting m or n can control the number of filter channels : When increasing m or n, the number of channels of the filter within the operating frequency range increases.

4. When m=n, the spectral band characteristic of the multi-channel filter is that pass bands and forbidden bands are alternately arranged to form multiple channels, and the filter channel bandwidths are equal.

5. Adjust the center frequency f of the working frequency band by adjusting the size of the filter, specifically:

Among them, v is the speed of sound in the air, d is the average diameter of rings A and B, and k _n is the zero point of the zero-order Bessel function.

Beneficial effects of the present invention: the present invention designs a multi-channel filter by utilizing the excellent physical properties and rich bandgap structure of the quasi-periodic structure. The multi-channel filter based on the quasi-periodic structure is a hollow tubular structure composed of two rings with different diameters coaxially arranged in a quasi-periodic sequence. According to the quasi-periodic structure of the generalized Fibonacci sequence arrangement, its spectral band characteristic is that pass bands and forbidden bands are alternately arranged to form multiple channels, and the filter channel width is uniform. The number of filtering channels of the filter can be adjusted by adjusting the algebra and the number of layers of the generalized Fibonacci sequence. The operating frequency band of the filter can also be adjusted by scaling up or down. The beneficial effect of the invention is that the filter is based on a quasi-periodic structure and has the function of multi-channel filtering. Compared with conventional filters based on periodic structures, filters based on quasi-periodic structures have more filtering channels due to the rich bandgap structure of the quasi-periodic structures. Both the number of filtering channels and the channel width of the filter can be regulated by controlling the algebra and the number of layers of the generalized Fibonacci sequence, so that the filter has a multi-channel tunable filtering function. The filter with a hollow tubular structure can ensure a good filtering effect while not obstructing the air flow. In addition, the hollow structure has a simple manufacturing process, and greatly reduces the cost of materials for making filters, so it has very broad application prospects in the fields of acoustic wave control and filters.

Description of drawings

FIG. 1 is a structural schematic diagram of a multi-channel filter based on a quasi-periodic structure. A hollow tubular structure composed of two rings of different diameters arranged coaxially in a quasi-periodic sequence. The circle with the smaller diameter is labeled A and the circle with the larger diameter is labeled B. Rings A and B have diameters d _A and d _B respectively. The length of A and B is equal to L.

Fig. 2 is the transmission spectrum of the quasi-periodic filter with 3 layers of the third generation generalized Fibonacci sequence.

Fig. 3 shows how the number of filtering channels and the filtering frequency range of the filter vary with the number of layers of the third-generation generalized Fibonacci sequence.

Detailed ways

The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments.

The multi-channel filter based on the quasi-periodic structure of the present invention is a waveguide structure whose internal structure is arranged in a quasi-periodic sequence. Its band structure has the characteristics of alternate distribution of multiple pass bands and forbidden bands. The quasi-periodic structure waveguide structure is a hollow tubular structure composed of two rings with different diameters coaxially arranged in a quasi-periodic sequence. The quasi-periodic sequence on which the internal structure of the waveguide is arranged is the generalized Fibonacci sequence. The band structure of the filter has multiple filter channels with uniform channel width. Adjusting the number of layers and algebra of the generalized Fibonacci sequence can adjust the number of filtering channels and the width of the filtering channel of the filter. The tube wall of the quasi-periodic structure waveguide has a certain thickness, usually not less than 4 mm. The pipe wall material generally adopts materials with high acoustic impedance, such as stainless steel, polyethylene resin and concrete. Changing the size of the waveguide structure proportionally can change the operating frequency range of the filter.

In the schematic diagram of a filter based on a quasi-periodic structure in FIG. 1 , the quasi-periodic structure is a hollow tubular structure formed by coaxially arranging two rings with different diameters in a quasi-periodic sequence. The basic units constituting the quasi-periodic structure are ring A with a smaller diameter and ring B with a larger diameter. The diameter d A of _A and the diameter d _B of B are 55mm and 85mm respectively. The length of A and B is equal to 175mm, denoted as L. The operating frequency f of the filter can be adjusted according to the following formula:

Among them, v is the speed of sound 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, when n=0, 1, 2..., k _n =0, 3.8317, 7.0156….

The unit arrangement in the quasi-periodic structure satisfies the generalized Fibonacci sequence, and its recursive relationship is:

Then the quasi-periodic structure is arranged according to the recurrence relation as:

或/>

or />

Here, m and n are any two positive integers. As long as the recurrence relationship of the above-mentioned generalized Fibonacci sequence is satisfied, the number of channels of the filter can be designed according to the actual filtering needs. In order to ensure that the filter channel bandwidth is equal to achieve a good filtering effect, m and n should be guaranteed to be equal. In this case, we call m or n the number of layers of the generalized Fibonacci sequence. For example, when m=n=3 (the number of layers is 3), the third-generation structural arrangement of the generalized Fibonacci sequence is S ₃ =BBBAAABBBAAABBBAAABBBBBBBBBB. When m and n are not equal, the number of channels of the filter within the operating frequency range will be increased, but the bandwidth of the filtering channels will also become uneven. When the algebra of the generalized Fibonacci sequence is increased, the number of filtering channels remains unchanged, and the width of the filtering channel will be slightly narrowed. Therefore, the width of the filtering channel can be fine-tuned by adjusting the algebra of the generalized Fibonacci sequence.

In Fig. 2, the transmission spectrum of the filter based on the quasi-periodic structure shown in Fig. 1 in the frequency window of 0-1000 Hz is plotted. As shown in the figure, in the frequency window of 0-1000Hz, three channels with high filtering effect appear. The frequency ranges of the three filter channels are: 69-254Hz, 392-576Hz and 715-898Hz. Therefore, the widths of the three filtering channels are 185Hz, 184Hz, and 183Hz, respectively. The channel width is very uniform and does not vary by more than 2Hz.

In Fig. 3, the number of filtering channels, the filtering frequency range and the number of filter layers based on the quasi-periodic structure are shown. The number of 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 filtering frequency range of the filtering channel when the number of layers of the quasi-periodic structure increases from 2 to 7 is listed. It is obvious from the figure that the number of 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 requirements, the number of filtering channels and the filtering frequency range of the filter are adjusted by adjusting the number of layers of the quasi-periodic structure, thereby realizing the function of multi-channel tunable filtering.

Claims (1)

1. A multi-channel filter based on a quasi-periodic structure, characterized in that: it is a waveguide structure arranged according to a quasi-periodic sequence, and the quasi-periodic sequence is a generalized Fibonacci sequence, and the waveguide structure is composed of two A hollow tubular structure in which rings of different diameters are coaxially arranged in a quasi-periodic sequence; the arrangement rule of the generalized Fibonacci sequence is specifically: the ring with the smaller diameter among the two rings with different diameters is A , the ring with a larger diameter is B, and the lengths of A and B are equal and L; the recurrence relationship of the two ring 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, />

It represents that the filter structure is m consecutively arranged kth generation structures S _k and then arranges n consecutively arranged k-1th generation S _k-1 structures; adjusting the algebra of the generalized Fibonacci sequence can control the filter The width of the filter channel: when increasing the algebra of the generalized Fibonacci sequence, the width of the filter channel becomes narrower; adjusting m or n can control the number of filter channels: when increasing m or n, the filter within the operating frequency range The number of channels increases; when m=n, the spectral band characteristics of the multi-channel filter are alternately arranged to form a plurality of channels for passbands and forbidden bands, and the filter channel bandwidths are equal; the center of the operating frequency band is adjusted by adjusting the size of the filter The frequency f, specifically:

Among them, v is the speed of sound in the air, d is the average diameter of rings A and B, and k _n is the zero point of the zero-order Bessel function.

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