Low-frequency wave-transmitting and high-frequency reflecting device based on frequency selective surface and satellite antenna housing
By designing a multi-layer structure in the FSS structure, using inter-layer coupling to achieve low-frequency ultra-wideband wave transmission and high-frequency ultra-wideband reflection, the problem that the existing FSS structure cannot take into account both low-frequency wave transmission and high-frequency reflection, providing high selectivity and excellent stealth performance.
Patent Information
- Application Number
- CN202411836314.5
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2024-12-13
- Publication Date
- 2025-03-21
- Estimated Expiration
- 2044-12-13
AI Technical Summary
The existing FSS structures have shortcomings in broadband wave transmission and reflection performance, and are especially unable to take into account low-band wave transmission and high-band reflection.
The multi-layer structural design is adopted, including the first low-pass layer, the first dielectric isolation layer, the first band-resistance layer, the second dielectric isolation layer and the second low-pass layer. The generation of transmission poles is achieved through inter-layer coupling, ensuring the rapid transition of ultra-wideband.
It realizes low-frequency ultra-wideband wave transmission and high-frequency ultra-wideband reflection, with high selectivity, and can provide better performance in the field of radar antenna stealth.
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Figure CN119674555A_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the technical field of satellite frequency selective surface antenna covers, and in particular relates to a low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface and a satellite antenna cover. Background Art
[0002] Radar cross section is an important indicator for evaluating the stealth performance of a target, which reflects the strength of the radar detection echo. For large platforms such as satellites and aircraft, the strong scattering of their radar antenna systems is the main contributor to the overall radar cross section. Traditional shape stealth technology and material stealth technology will have a very fatal impact on the radiation performance of the antenna, and it is difficult to meet the needs of the development of existing equipment.
[0003] Structural materials have both broadband wave transmission and reflection performance and load-bearing capacity, which makes them advantageous in the field of satellite antenna cover stealth. Frequency selective surface (FSS) is a periodic structure that has the performance of selective transmission, reflection and absorption of incident waves after loading loss devices, so the design is more flexible.
[0004] Generally, for the FSS design loaded on the satellite antenna cover, the single-layer FSS structure design will result in a narrow bandwidth of wave transmission and reflection of the overall structure, which cannot meet the application of the high frequency band of the satellite antenna cover. Therefore, it is necessary to provide an improved low-frequency wave transmission and high-frequency reflection device based on the frequency selective surface to solve the above problems. Summary of the invention
[0005] The purpose of the present invention is to provide a low-frequency wave-transmitting and high-frequency reflecting device and a satellite antenna cover based on a frequency selective surface, which utilizes the coupling effect between the band-stop layer and the low-pass layer to achieve the generation of transmission poles and ensure the rapid transition between ultra-widebands.
[0006] To achieve the above-mentioned purpose, the present invention provides a low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface, which comprises, from top to bottom, a first low-pass layer, a first dielectric isolation layer, a first band-stop layer, a second dielectric isolation layer and a second low-pass layer; the first low-pass layer and the second low-pass layer have the same structure and both comprise periodically arranged first metal patch patterns; each of the first metal patch patterns consists of four square ring patterns and one cross pattern, and the four square ring patterns are respectively connected to one end of the cross pattern;
[0007] The first band-blocking layer includes a periodically arranged second metal patch pattern.
[0008] Furthermore, the four square ring patterns are respectively located at four right-angled positions of a square, and the cross pattern coincides with the diagonal of the square; each end of the cross pattern is connected to the vertex of the corresponding square ring pattern, and the extension line of the cross pattern passes through the center of the square ring pattern connected thereto.
[0009] Furthermore, the width of each cross line of the cross pattern is equal to the width of each side of the square ring pattern. times, the length of each cross line is Wherein, W3 represents the width of each side of the square ring pattern, and S represents the distance between two adjacent square ring patterns.
[0010] Furthermore, the outer side length of each square ring pattern is 2.3-3.3 mm, the width W3 of each side of the square ring pattern is 0.2-0.4 mm, the spacing S between two adjacent square ring patterns in each first metal patch pattern is 0.7-1 mm; the distance between two adjacent first metal patch patterns is 0.3-0.5 mm.
[0011] Furthermore, the second metal patch pattern is a cross pattern, each cross line of the cross pattern has a length of 5.5-7.6 mm and a width of 0.2-0.4 mm, and a distance between two adjacent second metal patch patterns is 0.2-0.4 mm.
[0012] Furthermore, the first low-pass layer, the second low-pass layer and the first band-stop layer have the same arrangement period.
[0013] Furthermore, the first low-pass layer, the first band-stop layer, and the second low-pass layer further include dielectric substrates, respectively; the first metal patch pattern and the second metal patch pattern are periodically arranged on the dielectric substrates; the dielectric substrate of the first low-pass layer is adjacent to the first dielectric isolation layer; and the first metal patch pattern of the second low-pass layer is adjacent to the second dielectric isolation layer;
[0014] The dielectric substrate of the first band-blocking layer is adjacent to the second dielectric isolation layer.
[0015] Furthermore, the dielectric substrate is made of glass fiber reinforced epoxy resin material with a thickness of 0.15-0.25 mm; the first metal patch pattern and the second metal patch pattern are formed of metal copper.
[0016] Furthermore, the first dielectric isolation layer and the second dielectric isolation layer are made of aramid paper honeycomb material with a thickness of 1.8-2.2 mm.
[0017] The present invention also provides a radome, which is a frequency selective surface radome equipped with any of the above-mentioned low-frequency wave-transmitting and high-frequency reflecting devices.
[0018] In general, the above technical solution conceived by the present invention has the following technical advantages compared with the prior art:
[0019] 1. The present invention can solve the problem of narrow bandwidth and inability to balance low-frequency band transmission and high-frequency band reflection in the existing FSS structure by constructing a composite structure of a low-pass layer and a band-stop layer and making reasonable spatial arrangements. The present invention utilizes the selectivity of FSS to incident electromagnetic waves, so that a specific frequency selective surface layer acts on the corresponding frequency band, and utilizes interlayer coupling to achieve a rapid transition from low-frequency band to high-frequency band, ensuring ultra-wideband transmission frequency within the band and ultra-wideband reflection frequency outside the band, and has the characteristics of high selectivity.
[0020] 2. The wave transmission band of the present invention is mainly for the S band, and the reflection band is mainly for the Ka band. The design mode is simple, easy to assemble, light weight, low cost, and the wave transmission band and reflection band are wide. Through the design of the metal patch pattern, the first low-pass layer and the second low-pass layer have the transmission characteristics of wave transmission-reflection at high frequencies; the first band-stop layer has the transmission characteristics of wave transmission-reflection-wave transmission. Therefore, the first low-pass layer, the first band-stop layer and the second low-pass layer mainly realize low-frequency broadband wave transmission and high-frequency broadband reflection through the effect of interlayer coupling; the first low-pass layer and the second low-pass layer reflect at high frequencies of 22.93 to 40 GHz, transmit at 1 to 4.33 GHz, and the second band-stop layer transmits at 1 to 18 GHz.
[0021] 3. The present invention can independently design a transflective device with low-frequency wave transmission and high-frequency reflection performance according to the stealth requirements of low-frequency bands and high-frequency bands. By optimizing the shape and size of the metal patch pattern on the frequency-selective surface, the resonance point can be changed, thereby accurately regulating the wave transmission and reflection frequencies. BRIEF DESCRIPTION OF THE DRAWINGS
[0022] Figure 1 It is a structural schematic diagram of a unit pattern in a low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface provided in an embodiment of the present invention;
[0023] Figure 2 1 is a schematic structural diagram of a low-pass layer and a band-stop layer in a low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface provided by an embodiment of the present invention; (a) a first metal patch pattern corresponding to the first low-pass layer and the second low-pass layer, (b) a second metal patch pattern corresponding to the first band-stop layer;
[0024] Figure 3It is a first metal patch pattern in which a first low-pass layer and a second low-pass layer are periodically arranged in a low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface provided by an embodiment of the present invention;
[0025] Figure 4 It is a second metal patch pattern in which the first band-stop layer is periodically arranged in the low-frequency wave-transmitting and high-frequency reflecting device based on the frequency selective surface provided by an embodiment of the present invention;
[0026] Figure 5 It is a schematic diagram of the layer structure of a low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface provided by an embodiment of the present invention;
[0027] Figure 6 It is the transmission reflection characteristic of the embodiment of the present invention.
[0028] Throughout the drawings, the same reference numerals are used to denote the same elements or structures, wherein:
[0029] 1-first low-pass layer; 11-first metal patch pattern A; 12-first dielectric substrate; 2-cross pattern A; 3-square ring pattern A; 4-first dielectric isolation layer; 5-first band-stop layer; 51-second metal patch pattern; 52-second dielectric substrate; 6-cross pattern; 7-second dielectric isolation layer; 8-second low-pass layer; 81-first metal patch pattern B; 82-third dielectric substrate; 9-cross pattern B; 10-square ring pattern B. DETAILED DESCRIPTION
[0030] In order to make the purpose, technical scheme and advantages of the present invention clearer, the present invention is further described in detail below in conjunction with the embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention. In addition, the technical features involved in the various embodiments of the present invention described below can be combined with each other as long as they do not conflict with each other.
[0031] like Figure 1-6 As shown, the present invention provides a wave transmission and reflection device loaded on a satellite antenna cover, specifically a low-frequency wave transmission and high-frequency reflection device based on a frequency selective surface, which includes, from top to bottom, a first low-pass layer 1, a first dielectric isolation layer 4, a first band-stop layer 5, a second dielectric isolation layer 7, and a second low-pass layer 8. The first low-pass layer 1 and the second low-pass layer 8 have the same structure and both include a periodically arranged first metal patch pattern ( Figure 5 The first metal patch pattern A11 and B 81); each first metal patch pattern consists of four square ring patterns ( Figure 1 A3 and B10) and a cross pattern ( Figure 1The first band-stop layer 5 comprises a periodically arranged second metal patch pattern 51. The low frequency of the low-frequency wave transmission of the present invention generally refers to below 20 GHz (excluding 20 GHz), preferably 1-20 GHz, and the high frequency of the high-frequency reflection generally refers to above 20 GHz (including 20 GHz), preferably 20-45 GHz.
[0032] With such an arrangement, the coupling effect between the band-stop layer and the low-pass layer is utilized to realize the generation of transmission poles, thereby ensuring low-frequency ultra-wideband wave transmission and high-frequency ultra-wideband reflection.
[0033] like Figure 2 As shown in (a) (the yellow part represents metal copper), the structure and size of the first low-pass layer 1 and the second low-pass layer 8 are the same. Taking the first low-pass layer 1 as an example, the first low-pass layer 1 is a single-sided copper-clad board, and the copper foil is processed with a first metal patch pattern A 11 arranged periodically in rows and columns, as shown in FIG. Figure 3 , each first metal patch pattern A11 includes four square ring patterns A3 and one cross pattern A2; for any four square ring cross patterns (first metal patch pattern A11) in the array, there is a gap P-2*DS between two adjacent first metal patch patterns A11 (the existence of the resonance point can be changed by changing the gap width), and the four square ring patterns A3 are connected after rotating 45° through the cross pattern A2 (that is, the four square ring patterns A3 are respectively located at the four corners of a square, and the cross pattern A2 coincides with the diagonal of the square; the ends of the cross pattern A2 are connected to the top corners of the four square ring patterns A3, and the extension line of the cross pattern A2 passes through the center of the square ring pattern A3 connected thereto), thereby forming a first layer of low-pass layer FSS units, and the first layer of low-pass layer FSS unit array period P is 6-8mm (one period is composed of the first metal patch pattern A11 and the gap width of the edge, and the gap between two adjacent first metal patch patterns A11 is 6-8mm). The gap P-2*DS between 11 is the width of two slit widths).
[0034] like Figure 2 In (a), the width of each cross line of the cross pattern A2 is equal to the width W3 of each side length of each square ring pattern A3. times, the length of each cross line is S, wherein W3 represents the width of each side of the square ring pattern, and S represents the distance between two adjacent square ring patterns.
[0035] The outer side length D of each square ring pattern A3 is 2.3-3.3 mm, the width W3 of each side of the square ring pattern A3 is 0.2-0.4 mm, the spacing S between two adjacent square ring patterns in each first metal patch pattern is 0.7-1 mm; the distance between two adjacent first metal patch patterns is 0.3-0.5 mm.
[0036] like Figure 2 (b) and Figure 4 The first band-blocking layer 5 is a single-sided copper-clad board, and a second metal patch pattern 51 arranged periodically in rows and columns is processed on the copper foil, and each second metal patch pattern 51 includes a cross pattern 6; two adjacent cross patterns 6 in the array are not directly connected, but have a gap, thereby forming a first band-blocking layer FSS unit, and the array period P of the first band-blocking layer FSS unit is 6-8mm (one period consists of a second metal patch pattern 51 and the edge gap width W2).
[0037] The second metal patch pattern is a cross pattern, the length of each cross line of the cross pattern is P-W2=5.5-7.6mm, the width W1 is 0.2-0.4mm, and the distance 2W2 between two adjacent second metal patch patterns is 0.2-0.4mm.
[0038] In particular, the dielectric substrates used in the first low-pass layer 1, the first band-stop layer 5 and the second low-pass layer 8 are glass fiber reinforced epoxy resin materials with a thickness of 0.2 mm; the first dielectric isolation layer 4 and the second dielectric isolation layer 7 are both made of aramid paper honeycomb materials with a thickness of 2 mm; the cross pattern A 2, the four square ring patterns 3, the cross pattern 6, the cross pattern 9 and the four square ring patterns B10 are all thin sheets made of metal copper. Through the printed circuit board (PCB) processing technology, the first low-pass layer 1, the first band-stop layer 5 and the second low-pass layer 8 are made on the single-sided copper-clad board to form the corresponding FSS unit array, and the corresponding patterns are placed face down on the upper surface of the corresponding dielectric isolation layer, such as Figure 5 As shown (of course, as Figure 1 As shown, the second low-pass layer 8, with the dielectric substrate facing upward and the pattern facing downward, is placed on the lower surface of the corresponding dielectric isolation layer); through overall structural simulation optimization, a special device with good wave transmission / reflection characteristics is realized.
[0039] The present invention performs a multi-layer design on the transmission band and reflection band of a single-layer FSS, thereby utilizing the principle of interlayer coupling to enable the transmission and reflection characteristics of the multi-layer structure FSS to achieve ultra-wideband transmission and ultra-wideband reflection. The design of the first low-pass layer and the second low-pass layer is relatively complex, and can achieve low-frequency narrow-band transmission and high-frequency ultra-wideband reflection; the structure of the first band-stop layer is relatively simple, and can achieve low-frequency ultra-wideband transmission band, medium-frequency reflection, and high-frequency transmission. By utilizing the interlayer coupling between the low-pass layer and the band-stop layer, the high-frequency electromagnetic wave transmission of the low-pass layer is suppressed, so that the overall structure has the effect of high-frequency ultra-wideband reflection; the low-frequency narrow-band transmission of the low-pass layer is widened, so that the whole structure has the effect of low-frequency ultra-wideband transmission.
[0040] The present invention utilizes the overall coordination of various layer structures in the device to achieve the transmission of electromagnetic waves in the microwave frequency band of 1 to 8 GHz and the reflection of electromagnetic waves in the microwave frequency band of 26 to 40 GHz.
[0041] Example 1
[0042] The first metal patch pattern A11 of the first low-pass layer 1 is a single-sided copper-clad board, and four square ring patterns A3 and a cross pattern A2 array arranged periodically in rows and columns are processed on the copper foil. The array period P is 6mm, the outer side length D of the square ring pattern is 2.5mm, the line width W3 of the square ring is 0.3mm, and the line width of the cross pattern rotated 45° in the middle is Right now Length is Right now The seam width S between the square rings is 0.6 mm, and the seam width on one side edge is (P-2*DS) / 2, i.e. 0.2 mm.
[0043] The first dielectric isolation layer 4 is made of aramid paper honeycomb material with a thickness of 2 mm, a relative dielectric constant of 1.07, and a dielectric loss tangent of 0.0017.
[0044] The second metal patch pattern 51 of the first band-blocking layer 5 is a single-sided copper-clad board, and an array of cross-shaped patterns 6 arranged periodically in rows and columns is processed on the copper foil. The array period P is 6 mm, the length P-W2 of the cross-shaped pattern is 5.7 mm, and the line width W1 is 0.3 mm.
[0045] The second dielectric isolation layer 7 is made of aramid paper honeycomb material with a thickness of 2 mm, a relative dielectric constant of 1.07, and a dielectric loss tangent of 0.0017.
[0046] The first metal patch pattern B 81 of the second low-pass layer 8 is a single-sided copper-clad board, and four square ring patterns B10 and a cross pattern B 9 array arranged periodically in rows and columns are processed on the copper foil. The array period P is 6mm, the outer side length D of the square ring pattern B10 is 2.5mm, the square ring line width W3 is 0.3mm, and the line width of the cross pattern B 9 rotated 45° in the middle is Right now Length is Right now The seam width S between the square rings is 0.6 mm, and the edge seam width is (P-2*DS) / 2, i.e. 0.2 mm.
[0047] In a microwave darkroom, the transmission and reflection characteristics of this embodiment are measured. The parameter characteristics are as follows: Figure 6 As shown in the figure, the horizontal axis is frequency and the vertical axis is reflectivity, where S11 represents the reflectivity of electromagnetic waves and S21 represents the transmittance of electromagnetic waves. The multi-layer structure FSS achieves transmittance at 1 to 12 GHz and has a good reflection effect at 26 to 40 GHz.
[0048] The present invention is designed so that the first low-pass layer 1 and the second low-pass layer 8 have the following transmission characteristics at high frequencies: wave transmission-reflection; the first band-stop layer 5 has the following transmission characteristics: wave transmission-reflection-wave transmission. Therefore, the first low-pass layer 1, the first band-stop layer 5 and the second low-pass layer 8 mainly realize low-frequency broadband wave transmission and high-frequency broadband reflection through the effect of interlayer coupling; the first low-pass layer 1 and the second low-pass layer 8 reflect at high frequencies of 22.93 to 40 GHz and transmit at 1 to 4.33 GHz, and the second band-stop layer 5 transmits at 1 to 18 GHz. In general, the present invention is a wave transmission / reflection device of a multi-layer low-pass band-stop composite structure, which can be independently designed into a transflective device with low-frequency wave transmission and high-frequency reflection performance according to the stealth requirements of low-frequency bands and high-frequency bands.
[0049] The wave transmission and reflection performance of the low-frequency wave transmission and high-frequency reflection device (wave transmission / reflection device loaded on the satellite antenna cover) based on the frequency selective surface of the present invention can be adjusted according to actual needs. Taking the first band-stop layer 5 as an example, according to the equivalent circuit principle and the wave transmission resonance point calculation formula Its wave transmission performance is determined by the product of the metal length (equivalent inductance L) and the gap size (equivalent capacitance C). Correspondingly, the methods for adjusting the wave transmission frequency are as follows: ① By keeping the size of the gap, i.e. the equivalent capacitance C, unchanged, the metal length, i.e. the equivalent inductance L, can be changed; ② By changing the width of the gap, i.e. the equivalent capacitance C, the adjustment effect can also be achieved; among them, method ① is the most convenient; the first low-pass layer is similar.
[0050] The present invention utilizes the selectivity of FSS to the incident electromagnetic wave, so that the specific frequency selective surface layer acts on the corresponding frequency band, and utilizes the interlayer coupling to realize the rapid transition from the low frequency band to the high frequency band, thereby ensuring the ultra-wideband transmission frequency within the band and the ultra-wideband reflection frequency outside the band, and has the characteristics of high selectivity. The steepness of the transition bandwidth is expressed as the relative transition bandwidth in the present invention. Indicates that, f -10dB Indicates the frequency at which -10dB occurs, f -1dB It represents the frequency at which -1dB is located, that is, the relative bandwidth K=0.035 where the wave transmission band transitions to the reflection band. It has the characteristics of high selectivity and has a good advantage in the high selectivity stealth of radar antennas.
[0051] In the present invention, the cross pattern A2, the four square ring patterns A3, the cross patch pattern 6, the cross pattern B9 and the four square ring patterns B10 are all thin sheets made of metal copper. Various materials used in the present invention, such as glass fiber reinforced epoxy resin materials, aramid paper honeycomb materials, etc., can all be commercially available materials. In addition to the above embodiments, the present invention can also use other dielectric materials with little change in relative dielectric constant, dielectric loss angle, relative magnetic permeability, and magnetic loss angle as substrates; the period of each layer structure can also be other values within the range of 6 to 8 mm. When the period value changes, the overall performance of the entire structure will also change accordingly. In addition, the periods of the two selected FSS structures can also be different from each other.
[0052] It will be easily understood by those skilled in the art that the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the protection scope of the present invention.
Claims
1. A low-frequency wave-transmitting and high-frequency reflecting device based on a frequency selective surface, characterized in that: The first low-pass layer and the second low-pass layer have the same structure and both include periodically arranged first metal patch patterns; each of the first metal patch patterns consists of four square ring patterns and one cross pattern, and the four square ring patterns are respectively connected to one end of the cross pattern; The first band-blocking layer includes a periodically arranged cross-shaped second metal patch pattern.
2. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 1, characterized in that: The four square ring patterns are respectively located at four right-angled positions of a square, and the cross pattern coincides with the diagonal of the square; each end of the cross pattern is connected to the vertex of the corresponding square ring pattern, and the extension line of the cross pattern passes through the center of the square ring pattern connected thereto.
3. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 2, characterized in that: The width of each cross line of the cross pattern is equal to the width of each side of the square ring pattern. times, the length of each cross line is Wherein, W3 represents the width of each side of the square ring pattern, and S represents the distance between two adjacent square ring patterns.
4. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 3, characterized in that: The outer side length of each square ring pattern is 2.3-3.3 mm, the width W3 of each side length of the square ring pattern is 0.2-0.4 mm, the spacing S between two adjacent square ring patterns in each first metal patch pattern is 0.7-1 mm; the distance between two adjacent first metal patch patterns is 0.3-0.5 mm.
5. The low-frequency wave-transmitting and high-frequency reflecting device according to any one of claims 1 to 4, characterized in that: The length of each cross line of the cross pattern of the second metal patch pattern is 5.5-7.6 mm, the width is 0.2-0.4 mm, and the distance between two adjacent second metal patch patterns is 0.2-0.4 mm.
6. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 5, characterized in that: The metal patch patterns of the first low-pass layer, the second low-pass layer and the first band-stop layer have the same arrangement period.
7. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 5, characterized in that: The first low-pass layer, the first band-stop layer, and the second low-pass layer further include dielectric substrates, respectively; the first metal patch pattern and the second metal patch pattern are periodically arranged on the dielectric substrates; the dielectric substrate of the first low-pass layer is adjacent to the first dielectric isolation layer; and the first metal patch pattern of the second low-pass layer is adjacent to the second dielectric isolation layer; The dielectric substrate of the first band-blocking layer is adjacent to the second dielectric isolation layer.
8. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 7, characterized in that: The dielectric substrate is made of glass fiber reinforced epoxy resin material with a thickness of 0.15-0.25 mm; the first metal patch pattern and the second metal patch pattern are formed of metal copper.
9. The low-frequency wave-transmitting and high-frequency reflecting device according to claim 1, characterized in that: The first medium isolation layer and the second medium isolation layer are made of aramid paper honeycomb material with a thickness of 1.8-2.2 mm.
10. A radome, characterized in that: The antenna cover is a frequency selective surface antenna cover equipped with the low-frequency wave-transmitting and high-frequency reflecting device described in any one of claims 1 to 9.
Citation Information
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