CN115051167A - 1-bit dual-frequency dual-channel independent programmable super surface - Google Patents

Abstract

The invention relates to a 1-bit dual-frequency dual-channel independent programmable super surface. Every two parallel rectangular metal strip patches are arranged on 4 sides of the medium layer in the super-surface unit; a first metal patch and a second metal patch which are orthogonal to each other are arranged at the center of the dielectric layer, and the center of the orthogonal metal patches is connected to a metal ground through a metal via hole; the first metal patch and the second metal patch are H-shaped metal patches; the sides of the first metal patch and the second metal patch are connected with the center position of the corresponding rectangular metal strip patch through a diode; the central position of the rectangular metal strip patch is sequentially connected to the first feed layer, the second feed layer and the metal ground through the metal through hole; constructing a rectangular coordinate system on the dielectric layer; the first feed layer is a feed layer along the x-axis direction; the second feed layer is a feed layer along the y-axis direction. The invention can realize independent adjustability of the reflection phase of the dual-frequency dual-polarized electromagnetic wave and independent programmability of the dual channels.

Description

A 1-bit dual-frequency dual-channel independently programmable metasurface

technical field

The invention relates to the field of wireless communication, in particular to a 1-bit dual-frequency dual-channel independently programmable metasurface.

Background technique

With the iteration and development of science and technology, in the field of wireless communication, human beings are no longer satisfied with the information transmission rate of the current network. For now, for 4G, 5G and 6G or even higher signals, its penetration ability is significantly reduced and its energy loss is significantly increased. Therefore, it is urgent to find a signal transmission scheme with high efficiency, good performance and low cost. It should be pointed out that there are three main subjects in current communication: source (sender), channel (transmission channel), and sink (receiver). Signals experience reflection, refraction, penetration, scattering, diffraction, and interference in wireless channels. A series of complex transmission process, it is difficult to carry out perfect transmission. In order to transmit signals more efficiently and conveniently, some communication experts usually enhance the capabilities of base stations and terminals, or optimize the networking architecture, and rack their brains to overcome the uncertainty of wireless channels.

Electromagnetic metamaterials are artificial composite structural functional materials, which are composed of periodic or aperiodic arrangements of three-dimensional subwavelength artificial unit structures with specific geometric shapes. Unlike electromagnetic metamaterials, metasurfaces can serve as the two-dimensional equivalent of metamaterials, that is, two-dimensional planar material structures. By designing cell structures and arrangements with different shapes, the amplitude, phase, polarization, and propagation characteristics of electromagnetic waves can be effectively regulated. Compared with passive metamaterials, using other active metamaterials such as PIN tubes, triodes, MEMS, graphene, temperature-sensitive devices, photosensitive devices, etc., can dynamically control multiple dimensions of electromagnetic waves in real time, so RIS Reconfigurable smart metasurfaces emerge as the times require. The applications of RIS metasurfaces in the current era include elimination of coverage blind spots, multi-stream transmission rank enhancement, edge coverage enhancement, indoor coverage, and new transceivers. At present, academia and industry are actively exploring the performance of the actual deployment of RIS, with a view to adopting it to solve the coverage problem of 5G millimeter wave, and also apply it in the terahertz frequency band in the future. It is believed that RIS, an innovative technology, will bring us more surprises in the future, and its application prospects will be wider. In this context, Reconfigurable Smart Surfaces (RIS) are seen as a promising technology.

Generally speaking, in order to improve signal coverage and performance, most communication base stations usually use dual-polarized transmit antennas. Therefore, whether the RIS is dual-polarized will directly affect the reception of reflected waves by the user's receiving antenna. Compared with single-polarized single-frequency metasurfaces, dual-frequency dual-polarized metasurfaces can achieve more complex functions, such as multi-channel multi-task information processing, polarization division multiplexing, and dual-polarization aperture sharing. However, some of today's metasurfaces are mostly static dual-polarization and tunable single-polarization, which greatly limits the versatility of metasurfaces and their applications in ultrafast switching, scanning systems, and multitasking information processing.

Based on the above background, it is urgent to provide a reconfigurable intelligent metasurface unit with independently adjustable dual-frequency dual-polarized electromagnetic wave reflection phase and a metasurface that can realize dual-channel independently programmable.

SUMMARY OF THE INVENTION

The purpose of the present invention is to provide a 1-bit dual-frequency dual-channel independently programmable metasurface, which can realize dual-frequency dual-polarized electromagnetic wave reflection phase independently adjustable and dual-channel independent programmable.

For achieving the above object, the present invention provides the following scheme:

A 1-bit dual-frequency dual-channel independently programmable metasurface, comprising: a plurality of metasurface units; each of the metasurface units includes: a dielectric layer, a first feeding layer, a second Feed layer and metal ground;

The four sides of the dielectric layer are provided with rectangular metal strips that are parallel to each other; the center of the dielectric layer is provided with a first metal patch and a second metal patch that are orthogonal to each other, and the orthogonal metal patch The center of the sheet is connected to the metal ground through a metal via hole; the first metal patch and the second metal patch have the same structure and are both H-type metal patches; the first metal patch and the second metal patch have the same structure. The side of the second metal patch is connected to the center of the corresponding rectangular metal strip through a diode; the center of the rectangular metal strip is sequentially connected to the first feed through metal vias layer, the second feeding layer and the metal ground; take the direction of the first metal patch in the dielectric layer as the x-axis direction, and take the direction of the second metal patch as the y-axis direction to construct a Cartesian coordinate system ;

The first feeding layer is a feeding layer along the x-axis direction;

The second feeding layer is a feeding layer along the y-axis direction.

Optionally, the relative dielectric constant of the dielectric layer is ε _r =2.65, and PTFE F4B with loss tangent tanδ = 0.001 is used.

Optionally, the first feeding layer and the second feeding layer use Rogers with loss tangent tanδ=0.004 and dielectric constant ε _r =2.65, and use PTFE with loss tangent tanδ=0.001 F4B.

Optionally, the material of the metal ground is copper.

Optionally, the shapes of the dielectric layer, the first feeding layer, the second feeding layer and the metal ground are all squares with the same size.

Optionally, the metal through holes, the rectangular metal strip patch, the first metal patch, the second metal patch and the feeder are all made of copper.

Optionally, the model of the diode is SMP1320.

According to the specific embodiments provided by the present invention, the present invention discloses the following technical effects:

The invention provides a 1-bit dual-frequency dual-channel independently programmable metasurface, each metasurface unit integrates a pair of diodes in the x and y axes of the dielectric layer respectively, and the on-off of the diode is controlled by controlling the on-off of the diode. Independent dual-frequency 1-bit phase modulation can be achieved in the two directions of the x and y axes. By introducing low-loss diodes, it can meet the 180° phase difference at dual frequencies while maintaining high energy efficiency. Compared with the traditional adjustable reflection array antenna, the present invention has the characteristics of having different functions under the irradiation of x-polarized and y-polarized electromagnetic waves, which greatly increases its design freedom and expands its application prospect. The mutually orthogonal first metal patch and second metal patch arranged at the center of the dielectric layer have independent phase responses under the irradiation of x-polarized and y-polarized electromagnetic waves through this structure, and the x-polarized The required stable phase difference and high reflection amplitude can still be maintained under the oblique incidence of y-polarized electromagnetic waves.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the accompanying drawings required in the embodiments will be briefly introduced below. Obviously, the drawings in the following description are only some of the present invention. In the embodiments, for those of ordinary skill in the art, other drawings can also be obtained according to these drawings without creative labor.

1 is a schematic structural diagram of each metasurface unit in a 1-bit dual-frequency dual-channel independently programmable metasurface provided by the present invention;

Figure 2 is a schematic structural diagram of a dielectric layer;

3 is a schematic structural diagram of a first feeding layer;

4 is a schematic structural diagram of a second feeding layer;

FIG. 5 is a schematic structural diagram of a metal ground;

FIG. 6 is a schematic diagram of the thickness structure of the metal ground;

Fig. 7 is the surface current diagram when the frequency is 4GHz along the x-axis polarization direction;

Fig. 8 is the surface current diagram when the frequency is 7GHz along the y-axis polarization direction;

9 is a cross-polarization amplitude diagram of a metasurface unit provided by the present invention;

Fig. 10 is the reflected wave amplitude diagram of 2 kinds of encoding states of the metasurface unit provided by the present invention under x, y axis polarization;

Fig. 11 is the reflected wave phase diagram of 2 kinds of encoding states of the metasurface unit provided by the present invention under x, y axis polarization;

12 is a reflected wave amplitude diagram of the metasurface unit provided by the present invention under oblique incidence;

Fig. 13 is the reflected wave phase diagram of the state of the metasurface unit provided by the present invention under oblique incidence;

14 is a schematic diagram of the overall structure of the metasurface provided by the present invention;

15 is a schematic diagram of a two-dimensional far-field simulated beam with different coding sequences under the excitation of x-polarized and y-polarized electromagnetic waves;

16 is a schematic diagram of a three-dimensional far-field simulated beam with different coding sequences under x-polarized and y-polarized electromagnetic wave excitation;

FIG. 17 is a schematic diagram of a three-dimensional far-field simulated beam with different coding sequences under the excitation of a left-handed circularly polarized electromagnetic wave.

Detailed ways

The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, but not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

The purpose of the present invention is to provide a 1-bit dual-frequency dual-channel independently programmable metasurface, which can realize dual-frequency dual-polarized electromagnetic wave reflection phase independently adjustable and dual-channel independent programmable.

In order to make the above objects, features and advantages of the present invention more clearly understood, the present invention will be described in further detail below with reference to the accompanying drawings and specific embodiments.

As shown in Figure 1, a 1-bit dual-frequency dual-channel independently programmable metasurface includes: a plurality of metasurface units; each metasurface unit includes: a dielectric layer 1, a first A feeding layer 2, a second feeding layer 3 and a metal ground 4; the material of the metal ground 4 is copper.

The four sides of the dielectric layer 1 are provided with rectangular metal strips that are parallel to each other; the center position of the dielectric layer 1 is provided with a first metal patch and a second metal patch that are orthogonal to each other. The center position of the metal patch is connected to the metal ground 4 through a metal via hole, which can be used as a signal line for DC bias, that is, a negative electrode.

The first metal patch and the second metal patch have the same structure and are both H-type metal patches; the sides of the first metal patch and the second metal patch pass through diodes to correspond to the corresponding The center position of the rectangular metal strip patch is connected; the center position of the rectangular metal strip patch is sequentially connected to the first feeding layer 2, the second feeding layer 3 and the metal through metal vias Ground 4: Using the direction of the first metal patch in the dielectric layer 1 as the x-axis direction, and using the direction of the second metal patch as the y-axis direction, a Cartesian coordinate system is constructed.

The first feeding layer 2 is a feeding layer along the x-axis direction.

The second feeding layer 3 is a feeding layer along the y-axis direction.

A feed line is respectively drawn out in the x-axis direction of the first feeding layer 2 and the y-axis direction of the second feeding layer 3 as the positive electrode of the DC bias signal line.

By adjusting the on-off of the diode in the orthogonal direction, the present invention independently realizes dual-frequency dual-polarization 1-bit phase modulation in two orthogonal polarization directions, and further decouples in the orthogonal polarization direction. The invention can realize the exclusive-OR logic operation of the spin control of the circularly polarized wave, construct a fixed-frequency large-angle double-beam scanning antenna, a dual-polarized aperture shared antenna, and the like.

In the dielectric layer 1, each pair of diodes loaded in the x and y directions can be controlled by two DC bias voltages to be turned on and off, thereby independently controlling the encoding unit to vertically incident electromagnetic waves in the x-polarization and y-polarization. 180° reflection phase difference under illumination and can be mapped to digital states 0 and 1, respectively. Then each electrically tunable coding unit has four digital states 0/0, 0/1, 1/0 and 1/1 at the dual frequency points, where the front slash indicates that it is irradiated by the x-polarized incident wave. The digital state under the slash indicates its digital state under the irradiation of the y-polarized incident wave.

The shape of the dielectric layer 1 , the first feeding layer 2 , the second feeding layer 3 and the metal ground 4 are all squares with the same size.

The material of the metal through hole, the rectangular metal strip patch, the first metal patch, the second metal patch and the feeder is all copper.

The type of the diode is SMP1320. When the diode is on, its equivalent RLC model is a 0.5Ω resistor and a 0.7nH inductor in series; when the diode is off, its equivalent RLC model is a 0.5nH inductor and a 0.24pF capacitor in series.

As shown in FIG. 2 , the inner and outer lengths of one H-type metal patch in the center position of the dielectric layer 1 are l ₂ and l ₁ , and the inner and outer widths are w ₂ and w ₁ . There are also _four rectangular metal strips with lengths and widths _of l3 and w3 around the two H-shaped metal patches placed at right angles to each other. The sides of each H-shaped metal patch are connected to the rectangular metal strips. Diodes are used to connect the patches, and a total of 4 diodes are required. The first dielectric layer 1 has a relative permittivity of ε _r =2.65, and adopts polytetrafluoroethylene F4B with loss tangent tanδ = 0.001. The side length of dielectric layer 1 is p, which also includes 5 circular metal through holes with radius r, 4 circular metal through holes on the periphery, a pair of circular metal through holes in the x direction and the second layer The first feeding layer 2 is connected, a pair of circular metal through holes located in the y direction are connected to the second feeding layer 3 of the third layer, and the circular metal through hole in the center is connected to the first layer of the dielectric layer 1. The orthogonal H-shaped metal patches are connected and penetrated to the fourth metal ground 4 .

As shown in Figure 3, the second layer is a feeding layer along the x-axis direction, its side length is p, and contains 5 circular metal through holes with a radius r, and the 4 peripheral circular metal through holes are located in the center The circular metal via has a length of r ₂ . The circular metal through hole in the center is connected with the mutually orthogonal H-shaped metal patch of the first layer, but not in contact with the pattern layer of the second layer, the non-contact distance is r ₁ , and the four circles located around The metal through holes are respectively connected with the four metal strip patches on the first layer. The circular metal through-holes along the x-axis are connected by a section of feeder, whose length and width are l ₄ and w ₄ , respectively. The second layer can use Rogers with loss tangent tanδ=0.004.

As shown in FIG. 4 , the third layer is a feeding layer along the y-axis direction, and its side length is p, and PTFE F4B with loss tangent tanδ=0.001 is used. There is a microstrip line with length p and width w ₄ along the y-axis direction, and a hole with radius r ₃ at the center of the microstrip line.

As shown in FIG. 5 , the fourth layer is a metal ground layer, and its side length is p, and the center is a circular metal through hole passing through the first to fourth layers, and the radius is r. FIG. 6 is a side view of the cell structure, and the thicknesses of the dielectric layer 1 are h ₁ , h ₂ and h ₃ , respectively.

The metals are all copper, and each pair of diodes loaded in the x and y directions can be controlled by two DC bias voltages to be turned on and off, so that the encoding unit can be independently controlled to be perpendicular to the x-polarization and the y-polarization. A reflection phase difference of 180° is achieved under the irradiation of incident electromagnetic waves and large-angle oblique incident electromagnetic waves, corresponding to digital states 0 and 1, respectively. Then each electrically tunable coding unit has four digital states 0/0, 0/1, 1/0 and 1/1 at 2 frequency points, where the front slash indicates that it is in the x-polarized incident wave The digital state under irradiation, after the slash indicates its digital state under the irradiation of the y-polarized incident wave.

The first layer includes 4 rectangular metal strips that are positioned parallel to each other at the edge of the unit and 2 H-shaped metal strips placed in the center orthogonal to each other, and the sides of the H-shaped metal strips are connected to the metal strip One diode is connected to the center of the patch. The intersection of the centers of the two mutually orthogonal H-type metal patches is connected to the fourth layer of metal ground 4 through metal vias, which can be used as a signal line for DC bias, that is, a negative electrode. A rectangular coordinate system is set based on the center of the first layer, and a feeder line is respectively drawn in the x direction of the second layer and the y direction of the third layer as the positive pole of the DC bias signal line. The amplitude of the RIS unit only changes slightly under oblique incidence, and the phase difference is still about 180° at the center frequency point, which greatly improves the angular stability of the RIS unit under x and y polarization oblique incidence.

The diode model is SMP1320. When the diode is on, its equivalent RLC model is a 0.5Ω resistor and a 0.7nH inductor in series; when the diode is off, its equivalent RLC model is a 0.5nH inductor and a 0.24pF capacitor in series. The independently adjustable units in the x and y directions can realize the decoupling between polarizations, and the units independently perform phase regulation at the two frequency points and the two polarization directions.

In FIGS. 1 to 6 , the final optimized value of each structural parameter of a dual-polarized 1-bit phase-independently adjustable reconfigurable intelligent metasurface unit of the present invention is determined from Table 1, and Table 1 is as follows:

Table 1

The invention overcomes the technical difficulty of decoupling between polarizations, that is, when the first pair of diodes in the x-polarization direction changes states, the amplitude and phase of the reflected waves in the y-polarization direction are not affected, and vice versa. In order to clarify the above point of view, CST electromagnetic simulation software is used to carry out full-wave simulations for the working modes of x-polarization and y-polarization respectively. By analyzing the surface current diagrams shown in Figures 7 and 8, it can be seen that for the electric field with polarization distribution in the x-axis direction, most of the surface current is concentrated on the metal patches on both sides of the diode in the x-axis direction, which are orthogonal to each other. There is almost no surface current on both sides of the diode in the y-direction. Similarly, when the electric field is polarized and distributed along the y-axis direction, the surface current distribution diagram shown in Fig. 7 is obtained, and the conclusion is similar to the above expression. It is thus confirmed that the diodes are decoupled in the x and y directions, that is, electromagnetic waves in the x-polarization direction have no effect on a pair of diodes in the y-polarization direction, and vice versa. As can be seen from the cross-polarization amplitude plot in Fig. 9, the cross-polarization of the proposed unit is less than -50dB, which in turn enables independent phase regulation of the unit in the x-polarization and y-polarization directions.

In order to further study the specific performance of the unit structure of the present invention, the incident angle is set to 0° and 30°, and full-wave simulation is carried out under the CST simulation software. Fig. 10 and Fig. 12 are the reflected wave amplitude diagrams of the two encoding states of the metasurface unit under the polarization of the x and y axes with the incident angles of 0° and 30°, respectively.

Fig. 11 and Fig. 13 are the reflected wave phase diagrams of the two encoding states of the metasurface unit under the polarization of the x and y axes with the incident angles of 0° and 30°, respectively. It can be seen from Fig. 9 and Fig. 11 that at the frequency points of 4 GHz and 7 GHz, under two different polarizations, the amplitude of the reflected wave in each state is greater than -1 dB. It can be seen from Figure 10 and Figure 12 that at the frequency points of 4GHz and 7GHz, under two different polarizations, the phase difference of the reflected waves in each state meets the required phase difference of 180° for 1 bit, and there is a wide range within the allowable error range. Band bandwidth. The letters On and Off in Figure 10 to Figure 13 represent the on and off states of the diode, respectively, Rxx and Ryy represent the x and y polarizations, respectively; Rxy and Ryx represent the respective cross polarizations; Phase_dif represents the diode when the x polarization Phase difference between on and off.

Figure 14 is a schematic diagram of a 1-bit dual-frequency dual-channel independently programmable metasurface structure constructed by metasurface units. By controlling the states of the diodes in the two orthogonal directions of x and y, circularly polarized wave spin can be realized Controlled XOR logic operation, construction of fixed-frequency large-angle dual-beam scanning antenna and dual-polarization aperture shared antenna, etc. In order to verify the performance of the designed unit, a dual-beam RIS composed of 24*24 adjustable units is constructed, and the overall size is 288mm*288mm. Under the x-polarized incidence, the corresponding code sequence S1 is "000000000000111111111111", the reflection angle can be calculated according to formula (1) generalized Snell's law, and the reflection angles at 4GHz and 7GHz frequency points are ±15.1°, ± 8.6°. Under y-polarized incidence, the corresponding code sequence S2 is "000000111111000000111111", and the reflection angles at 4GHz and 7GHz frequency points are calculated by formula (1) to be ±31.4° and ±17.3°, respectively.

θ=sin ^-1 (λ/Γ) (1)

In formula (1), λ represents the wavelength in free space (75 mm and 42.9 mm at 4 GHz and 7 GHz, respectively), and Γ represents the geometric length of the gradient phase distribution in one cycle. 15 is a simulation of the RIS metasurface constructed by the reconfigurable intelligent metasurface unit with dual-frequency dual-polarization 1-bit phase independently adjustable in the embodiment of the present invention, under the x and y polarization, the coding sequences at 4 GHz and 7 GHz are obtained Two-dimensional far-field pattern. 16 is a schematic diagram of a 1-bit dual-frequency dual-channel independently programmable metasurface structure constructed by a metasurface unit in an embodiment of the present invention. Under x polarization, when the coding sequence at 4GHz and 7GHz is S1, the obtained simulated three-dimensional remote Field pattern. Under the incidence of orthogonal x-polarized waves, the dual-beam scanning system measured two symmetrical beams pointing at ±16.5° and ±9° at 4GHz and 7GHz, respectively. Under the incidence of orthogonal y-polarized waves, the dual-beam scanning system measured two symmetrical beams pointing at ±29.5° and ±17.5° at 4GHz and 7GHz, respectively. The deviation between the beam pointing and the theoretical value is basically within 2°. The simulation results are basically consistent with the theoretical predictions. When this RIS metasurface is encoded using the encoding sequence [S1 S2] under LCP incidence, the simulation results in four distinct pencil beams, two of which are x-polarized (co-polarized in the y-z plane), pointing towards ±17.5°, with two y-polarized beams (co-polarized in the x-z plane) pointing at ±9°, Figure 17 shows the four distinct pencil beams obtained at 7 GHz.

The various embodiments in this specification are described in a progressive manner, and each embodiment focuses on the differences from other embodiments, and the same and similar parts between the various embodiments can be referred to each other.

In this paper, specific examples are used to illustrate the principles and implementations of the present invention. The descriptions of the above embodiments are only used to help understand the methods and core ideas of the present invention; meanwhile, for those skilled in the art, according to the present invention There will be changes in the specific implementation and application scope. In conclusion, the contents of this specification should not be construed as limiting the present invention.

Claims (7)

1. a 1-bit dual-frequency dual-channel independently programmable metasurface, characterized in that, comprising: a plurality of metasurface units; each described metasurface unit comprises: a dielectric layer, a first a feeding layer, a second feeding layer and a metal ground; The four sides of the dielectric layer are provided with rectangular metal strips that are parallel to each other; the center of the dielectric layer is provided with a first metal patch and a second metal patch that are orthogonal to each other, and the orthogonal metal patch The center of the sheet is connected to the metal ground through a metal via hole; the first metal patch and the second metal patch have the same structure and are both H-type metal patches; the first metal patch and the second metal patch have the same structure. The side of the second metal patch is connected to the center of the corresponding rectangular metal strip through a diode; the center of the rectangular metal strip is sequentially connected to the first feed through metal vias layer, the second feeding layer and the metal ground; take the direction of the first metal patch in the dielectric layer as the x-axis direction, and take the direction of the second metal patch as the y-axis direction to construct a Cartesian coordinate system ; The first feeding layer is a feeding layer along the x-axis direction; The second feeding layer is a feeding layer along the y-axis direction. 2 . The 1-bit dual-frequency dual-channel independently programmable metasurface according to claim 1 , wherein the relative permittivity of the dielectric layer is ε _r =2.65, and the loss tangent tanδ = 0.001 is used. 3 . of PTFE F4B. 3. The 1-bit dual-frequency dual-channel independently programmable metasurface according to claim 1, wherein the first feeding layer and the second feeding layer adopt loss tangent tanδ=0.004 The Rogers and dielectric constant of ε _r = 2.65, using teflon F4B with loss tangent tanδ = 0.001. 4 . The 1-bit dual-frequency dual-channel independently programmable metasurface according to claim 1 , wherein the metal ground is made of copper. 5 . 5 . The 1-bit dual-frequency dual-channel independently programmable metasurface according to claim 1 , wherein the dielectric layer, the first feeding layer, the second feeding layer and the metal ground have the same shape. 6 . All are squares of the same size. 6. The 1-bit dual-frequency dual-channel independently programmable metasurface according to claim 1, wherein the metal through hole, the rectangular metal strip, the first metal patch, the second metal The material of patch and feeder is copper. 7 . The 1-bit dual-frequency dual-channel independently programmable metasurface according to claim 1 , wherein the model of the diode is SMP1320. 8 .

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