CN118676619A - Pure metal anisotropic holographic impedance super-surface antenna and design method - Google Patents
Pure metal anisotropic holographic impedance super-surface antenna and design method Download PDFInfo
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Abstract
The invention also discloses a pure metal anisotropic holographic impedance super-surface antenna and a design method, because of the structural complementation characteristic of the pure metal structure and the patch structure with the dielectric substrate, the pure metal anisotropic holographic impedance super-surface antenna can be used for designing a pure metal structural unit only by changing the original angle corresponding to the long axis by 90 degrees into the angle corresponding to the short axis as a rotation angle according to the Barbie principle. By combining the holographic principle, the leaky wave theory and the Barbie principle, the mapping relation between the tensor impedance of the unit of the pure metal structure and the geometric parameters of the unit is directly calculated, and the anisotropic impedance holographic super-surface model of the pure metal is established. Compared with the non-flat pure metal modulated tensor impedance super surface, the pure metal spatial wave modulated transmitting array and the pure metal spatial wave modulated reflecting array which are realized by adopting the additive manufacturing process, the pure metal anisotropic impedance holographic super surface has the unique advantages of simple manufacture, ultra-small appearance, easy integration and the like.
Description
Technical Field
The invention belongs to the technical field of super-surface antennas, and particularly relates to a pure metal anisotropic holographic impedance super-surface antenna and a design method thereof.
Background
The supersurface consisting of periodic and aperiodic sub-wavelength meta-units is a two-dimensional planar structure, i.e. a metamaterial, derived from three-dimensional spatially structured electromagnetic materials. The metamaterial realizes the non-existing extraordinary electromagnetic medium parameters in the nature, and expands the degree of freedom of electromagnetic modulation. In addition, from the aspect of modulation function, the metamaterial can be divided into polarization modulation, frequency modulation, amplitude modulation and phase modulation, and is successfully applied to the fields of electromagnetic wave absorption, frequency selective surface radiators, stealth materials and the like, so that the problem that the traditional antenna is limited in function due to structural design is solved. The super-surface can be classified into a surface wave modulated super-surface and a spatial wave modulated super-surface according to the electromagnetic wave modulation mechanism. In spatial wave modulated supersurfaces, the most common application is gradient phase curvature, where abrupt phase changes can be produced by generalized snell's law. The spatial wave modulated super surface, consisting of gradient phase planes, can then be developed using ray tracing to develop a transmissive array and a reflective array. The reflective array increases the shielding of the outgoing wave compared to the transmitting array, since its feed is in the same space as the reflected wave, which limits its application.
The invention discloses a circular polarization non-diffraction electromagnetic wave antenna based on an anisotropic holographic impedance super surface, which solves the problem that the existing antenna can not generate electromagnetic waves with circular polarization and high beam focusing characteristics. However, the presence of a single dielectric plate can create leaks in other harsh environments (e.g., extreme cold and heat), thereby destroying the stability of the substrate dielectric constant and changing the strength of the dielectric, resulting in array distortion, affecting the overall performance of the antenna. In addition, the transmitting array without the dielectric layer can not only reduce dielectric loss, but also can be used as a lens to bear high-power microwave irradiation. The dual function has wide application prospect in the military field. Pure metal reflective arrays and transmissive arrays are proposed, the configuration of which includes four cascaded planar metal layers, three cascaded planar metal layers, two cascaded planar metal layers, and a single layer of metal, greatly improving the environmental adaptability and performance stability of the system.
Compared with the high system modulation caused by an external air feed structure which is indispensable to the super surface of the spatial wave modulation, the feed structure in the super surface of the surface wave modulation can be integrated with the surface of the super surface of the spatial wave modulation, so that the integration performance of the system is greatly improved. The most representative structure in the surface wave modulated super surface is a hologram impedance plane, which can be classified into an isotropic hologram impedance plane and an anisotropic hologram impedance plane according to the structural characteristics of the cell. In order to overcome adverse effects of severe environment and maintain performance indexes of the antenna, a holographic impedance surface of the pure metal modulation element surface antenna based on additive manufacturing is provided, and adaptability and adjustment capability of the antenna are expanded to a certain extent. However, the longitudinally non-uniform growth structure of the cells increases processing complexity while reducing the planar integration performance of the system.
The existing design method can only be applied to a structure of a metal patch with a dielectric substrate, when a pure metal structure is integrally adopted, the traditional design method is not applicable when the size of a unit is calculated, and the pure metal structure needs to additionally consider the connection relation between the metal structures.
Disclosure of Invention
The invention provides a redundant steering engine speed reducing device for an unmanned aerial vehicle, which solves the problems that the traditional design method is not applicable when calculating the size of a unit, and the connection relation between metal structures is required to be additionally considered for a pure metal structure.
In order to achieve the above purpose, the present invention provides the following technical solutions:
The pure metal anisotropic holographic impedance super-surface antenna comprises a transmission array, wherein a monopole antenna is arranged in the center of the transmission array, the transmission array comprises a plurality of impedance units which are arranged in an array manner, each impedance unit comprises a lower metal floor and an upper hollow metal plate, and an air layer is arranged between the two metal plates;
the upper metal plate of each unit consists of a round hollow and a rectangular metal structure penetrating through the hollow center, and an included angle is formed between the upper metal plate and the horizontal plane of the transmission array.
Preferably, the transmissive array comprises 49 x 49 impedance units.
Preferably, the thickness of the upper layer metal plate is the same as that of the lower layer metal plate, and the thickness of the air layer is 2 times that of the upper layer metal plate.
A design method of a pure metal anisotropic holographic impedance super-surface antenna comprises the following steps:
Determining the irradiation direction of the wave beam, and acquiring components of impedance tensors of each impedance unit according to the irradiation direction of the wave beam;
Acquiring the relation between the equivalent scalar impedance and the crawling direction of the surface wave according to the components of the impedance tensor of each impedance unit;
Drawing an elliptic curve according to the relation between the equivalent scalar impedance and the crawling direction of the surface wave;
Obtaining the maximum value of equivalent scalar impedance and the included angle between the upper metal plate and the horizontal plane of the transmission array according to the elliptic curve;
and obtaining the radius of the circular hollowed-out part according to the maximum value of the equivalent scalar impedance.
Preferably, the step of determining the irradiation direction of the beam and acquiring the component of the impedance tensor of each impedance unit according to the irradiation direction of the beam comprises:
where k z denotes the wave number in the Z-axis direction, k 0 denotes the wave number in free space, Is the normalized equivalent scalar impedance, Z xx,Zxy,Zyy is the three components of the impedance tensor Z, respectively.
Preferably, the impedance component is obtained from a surface current field of the monopole antenna on the impedance unit and an electric field of the monopole antenna.
Preferably, the components of the impedance tensor Z further include Z yx, which is a pure virtual matrix, Z xy=Zyx, according to the law of conservation of energy and the symmetry characteristics of the proposed element.
Preferably, the drawing of the elliptic curve according to the relationship between the equivalent scalar impedance and the crawling direction of the surface wave is specifically:
And for impedance units at different positions, obtaining a change curve of an equivalent isotropic impedance value of the anisotropic surface impedance along with different crawling angles theta k of the surface wave, wherein the change of the equivalent scalar impedance value of the surface wave in different propagation directions of the tensor impedance surface shows an elliptic curve form.
Preferably, the maximum value of the equivalent scalar impedance obtained from the elliptic curve is specifically:
The major axis of the elliptic curve corresponds to the maximum value of the equivalent scalar impedance.
Preferably, the included angle between the upper metal plate and the horizontal plane of the transmission array is the included angle between the long axis of the elliptic curve and the X axis plus 90 degrees.
Compared with the prior art, the invention has the following beneficial effects: the invention provides a pure metal anisotropic holographic impedance super-surface antenna which is characterized by comprising a transmission array, wherein a monopole antenna is arranged at the center of the transmission array, the transmission array comprises a plurality of impedance units which are arranged in an array mode, each impedance unit comprises a lower-layer metal floor and an upper-layer hollowed-out metal plate, an air layer is arranged between the two layers of metal plates, the upper-layer metal plate of each unit is formed by a round hollowed-out metal structure and a rectangular metal structure penetrating through the hollowed-out center, an included angle is formed between the upper-layer metal plate and the horizontal plane of the transmission array, and a pure metal flat structure is adopted to convert surface waves into leaky waves.
The invention also provides a design method of the pure metal anisotropic holographic impedance super-surface antenna, and the pure metal anisotropic holographic impedance super-surface antenna can be used for designing a pure metal structural unit by changing the original long axis corresponding angle by 90 degrees into the short axis corresponding angle as a rotation angle according to the Barbie's principle due to the structural complementation characteristic of the pure metal structure and the patch structure with the dielectric substrate. By combining the holographic principle, the leaky wave theory and the Barbie principle, the mapping relation between the tensor impedance of the unit of the pure metal structure and the geometric parameters of the unit is directly calculated, and the anisotropic impedance holographic super-surface model of the pure metal is established. Compared with the non-flat pure metal modulated tensor impedance super surface, the pure metal spatial wave modulated transmitting array and the pure metal spatial wave modulated reflecting array which are realized by adopting the additive manufacturing process, the pure metal anisotropic impedance holographic super surface has the unique advantages of simple manufacture, ultra-small appearance, easy integration and the like.
Drawings
Fig. 1 is a schematic diagram of the overall structure of an antenna part according to an embodiment of the present invention, including a monopole antenna and a holographic impedance modulation surface.
Fig. 2 is a schematic diagram of the tensor impedance unit structure.
Fig. 3 is an equivalent scalar impedance corresponding to the surface wave propagation angle θ k on a cell with a narrow metal cuboid width g s =2 mm, radius R s =5 mm, rotation angle θ s =60.
Fig. 4 is a graph of maximum equivalent scalar impedance versus different cylinder hollow radii R s.
Fig. 5 shows the distribution of the invented anisotropic holographic impedance plane for parameter R s at 7.5GHz single beam operation.
Fig. 6 shows the distribution of the invented anisotropic holographic impedance plane for the parameters theta s at 7.5GHz single beam operation.
Fig. 7 shows the distribution of the invented anisotropic holographic impedance plane for the parameter R s at 7.5GHz dual beam operation.
Fig. 8 shows the distribution of the invented anisotropic holographic impedance plane for the parameters theta s at 7.5GHz dual beam operation.
Fig. 9 (a) is a 3D far-field radiation pattern simulated at 7.5GHz for a single-beam anisotropic holographic impedance surface, and fig. 9 (b) is a 3D far-field radiation pattern simulated at 7.5GHz for a dual-beam anisotropic holographic impedance surface.
Fig. 10 is a simulated and measured far-field radiation pattern of the inventive single beam anisotropic holographic impedance plane at 7.5 GHz.
Fig. 11 is a simulated and measured far-field radiation pattern of the inventive dual-beam anisotropic holographic impedance plane at 7.5 GHz.
Fig. 12 is S11 of the inventive single beam anisotropic holographic impedance surface in operation.
Fig. 13 is S11 of the inventive dual beam anisotropic holographic impedance surface in operation.
In the figure, 1-upper layer hollowed-out metal plate, 2-monopole antenna and 3-metal floor
Detailed Description
For the purpose of making the objects, technical solutions and advantages of the embodiments of the present invention more apparent, the technical solutions of 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, and it is apparent that the described embodiments are some embodiments of the present invention, but not all embodiments of the present invention. The components of the embodiments of the present invention generally described and illustrated in the figures herein may be arranged and designed in a wide variety of different configurations.
Thus, the following detailed description of the embodiments of the invention, as presented in the figures, is not intended to limit the scope of the invention, as claimed, but is merely representative of selected embodiments of the invention. All other embodiments, which can be made by those skilled in the art based on the embodiments of the invention without making any inventive effort, are intended to be within the scope of the invention.
It should be noted that: like reference numerals and letters denote like items in the following figures, and thus once an item is defined in one figure, no further definition or explanation thereof is necessary in the following figures.
In the description of the embodiments of the present invention, it should be noted that, if the terms "upper," "lower," "horizontal," "inner," and the like indicate an azimuth or a positional relationship based on the azimuth or the positional relationship shown in the drawings, or the azimuth or the positional relationship in which the inventive product is conventionally put in use, it is merely for convenience of describing the present invention and simplifying the description, and does not indicate or imply that the apparatus or element to be referred to must have a specific azimuth, be configured and operated in a specific azimuth, and thus should not be construed as limiting the present invention. Furthermore, the terms "first," "second," and the like, are used merely to distinguish between descriptions and should not be construed as indicating or implying relative importance.
Furthermore, the term "horizontal" if present does not mean that the component is required to be absolutely horizontal, but may be slightly inclined. As "horizontal" merely means that its direction is more horizontal than "vertical", and does not mean that the structure must be perfectly horizontal, but may be slightly inclined.
In the description of the embodiments of the present invention, it should also be noted that, unless explicitly specified and limited otherwise, the terms "disposed," "mounted," "connected," and "connected" should be construed broadly, and may be, for example, fixedly connected, detachably connected, or integrally connected; can be mechanically or electrically connected; can be directly connected or indirectly connected through an intermediate medium, and can be communication between two elements. The specific meaning of the above terms in the present invention can be understood by those of ordinary skill in the art according to the specific circumstances.
In order to make the technical scheme of the present invention better understood by those skilled in the art, the present invention will be further described in detail with reference to the accompanying drawings.
The invention provides an ultrathin pure metal anisotropic impedance holographic super surface with low cost for the first time, and explores in the C-band radio frequency range. In order to better adapt to severe conditions of extreme cold and extreme heat and possibly realize radiation modulation of high-power microwaves, the invention abandons the super surface based on a substrate in the traditional Printed Circuit Board (PCB) process and adopts a pure metal plane structure to convert the surface waves into leaky waves.
As shown in fig. 1, the invention provides a pure metal anisotropic holographic impedance super-surface antenna, which comprises a transmission array, wherein a monopole antenna is arranged in the center of the transmission array, the transmission array comprises a plurality of impedance units which are arranged in an array manner, each impedance unit comprises a lower metal floor and an upper hollow metal plate, and an air layer is arranged between the two metal plates;
the upper metal plate of each unit consists of a round hollow and a rectangular metal structure penetrating through the hollow center, and an included angle is formed between the upper metal plate and the horizontal plane of the transmission array.
The upper metal plate of each unit consists of a circular hollow with a radius of R s and a narrow rectangular metal structure with a rotatable rotation angle of theta s passing through the center of the hollow. The round hollowed-out sizes of the upper layers of the different impedance units are different from the rotation angles of the narrow rectangles.
The geometry shown in fig. 2 shows a period of p=16 mm, a thickness of 1mm for two metal plates and a height of 2mm for the middle air layer
The design adopts a monopole antenna with the working frequency of 7.5GHz and a quarter wavelength to excite, and the monopole antenna surface current field is given by the following formula:
Wherein, A position vector representing the central geometric position of the m-th row and n-th column of the hypersurface unit on the anisotropic holographic impedance hypersurface; (x mn,ymn, 0) represents the position coordinates of the m-th row and n-th column of the super surface unit on the super surface, and n e is the equivalent refractive index of the modulated anisotropic holographic impedance plane.
When a monopole antenna is placed as a feed source at the origin of the XOY plane, its electric field is given by formula two:
wherein (1, 0) indicates that the polarization direction of the radiation wave is along the x-axis, Is the wave vector of the i-space beam.
Tensor impedance expression formula III which simultaneously satisfies the law of conservation of energy and the reciprocity theorem:
Where X represents the average modulation impedance and M represents the average modulation depth, determined by the maximum equivalent scalar impedance and the minimum equivalent scalar impedance. Here the number of the elements is the number, Represents the vector outer product and represents the conjugate transpose.
Substituting the first and second formulas into the third formula, and determining the irradiation direction of the design beamThereafter, for the m-th row, n-th column of the supersurface elements, the three components Z xx,Zxy,Zyy of the impedance tensor Z can be given by:
considering the law of conservation of energy and the symmetry characteristics of the proposed unit, the non-hermite matrix Z must satisfy the reciprocity theory, requiring that Z be a pure virtual matrix, letting the component Z xy=Zyx.
In order to simplify the calculation of the relationship between the element impedance tensor and its own geometric parameters and to further clarify the propagation rule of the surface wave on the symmetrical tensor impedance surface element, we can get equation four for a given tensor impedance Z and surface wave propagation direction θ k:
where k z denotes the wave number in the Z-axis direction, k 0 denotes the wave number in free space, Is the normalized equivalent scalar impedance. To this end, according to equation four, we can determine the equivalent scalar impedance by the specific tensor impedance component Z xx,Zxy,Zyx,Zyy And the surface wave crawling direction theta k.
As shown in fig. 3, for units at different positions, we can obtain the variation curve of the equivalent isotropic impedance value of the anisotropic surface impedance with different crawling angles θ k of the surface wave. The change in the equivalent scalar impedance value of the surface wave in different propagation directions of the tensor impedance surface takes the form of an elliptic curve.
In a conventional substrate-based non-pure metal supersurface unit, the major axis of the elliptical impedance curve corresponds to the maximum Z emax of the equivalent scalar impedance, and the angle between the major axis and the x-axis is equal to the slot angle θ s of the design unit. However, in the present design, there is an additional 90 degree difference between the angle θ s of the rectangular metal plate and the major axis angle of the equivalent scalar impedance elliptic curve. This difference is mainly due to the complementary structural features between this pure planar metal tensor cell and the conventional substrate-based rectangular slot design, which can be explained by the babbitt principle.
To this end we obtain the maximum value of the equivalent scalar impedance for each location of the designed subsurface. The maximum value Z emax of the equivalent scalar impedance is only determined by the cylindrical hollow radius R s, and for units with different cylindrical hollow radii R s, the performance of the unit can be obtained by simulation through CST simulation software, and as shown in fig. 4, a simple mapping relationship between the impedance tensor and the geometric parameters of the designed unit is established.
To sum up, determine the feed source and the design beam irradiation directionThen, three components Z xx,Zxy,Zyy of the impedance tensor Z at different positions on the array can be obtained. Then we can get an equivalent scalar impedanceAnd the crawling direction theta k of the surface wave, the long axis of the formed image corresponds to the maximum value Z emax of equivalent scalar impedance, and the included angle between the long axis and the x axis is added by 90 degrees to be equal to the groove angle theta s of the design unit. And finally, by comparing the results of unit simulation under different hollow cylinder radiuses, finding the cylinder hollow radius R s corresponding to the maximum equivalent scalar impedance. The rotation angle theta s of the unit rectangular metal structure at different positions and the radius R S of the cylindrical hollow structure can be obtained.
Two anisotropic holographic impedance super-surface antennas are designed in the invention: is a broadside single beamThe other is a double beam in which the pencil beam #1 is directedPencil beam #2 pointingThe entire supersurface consists of 49 x 49 units with pore sizes of 784mm x 784mm. The novel floor consists of an upper layer of metal plate and a lower layer of metal plate, wherein the lower layer is a pure metal floor with the thickness of 1mm, the upper layer is a metal plate cut with patterns, the thickness of the upper layer is 1mm, and the thickness of an air interval between the two layers is 2mm. From the above equation, E obj and J ref, which are distributed at different positions on two modulated anisotropic holographic impedance surfaces operating at 7.5GHz frequency, can be calculated, followed by calculation of tensor impedance component Z. Further, considering the equivalent scalar equation and the mapping relationship between the maximum equivalent scalar impedance and the cylinder hollow radius, the geometric parameters R s and θ s can be obtained as shown in fig. 5,6,7, 8.
On the other hand, specific parameters of the monopole feed antenna are as follows. The monopole feed antenna may be a cylindrical metal monopole antenna. The length of the monopole antenna adopted by the invention is 10mm, the diameter is 1.8mm, and the monopole antenna passes through a cylindrical hole with the middle radius of 5mm on the super surface to feed the whole antenna;
The above cases are simulated in conjunction with the electromagnetic simulation software HFSS.
Simulation 1, a 2D far field pattern of a single beam pure metal anisotropic impedance holographic super surface in an embodiment of the invention is simulated, and the result is shown in fig. 10.
Simulation 2, a 2D far field pattern of a single beam pure metal anisotropic impedance holographic super surface in an embodiment of the invention is simulated, and the result is shown in fig. 11.
Simulation 3, the simulation of the S11 parameter of the single beam pure metal anisotropic impedance holographic super surface in the embodiment of the invention is shown in fig. 12.
Simulation 4, the simulation of the S11 parameter of the single beam pure metal anisotropic impedance holographic super surface in the embodiment of the invention is shown in fig. 13.
Simulation and test result analysis
As shown in fig. 9 (a), 9 (b), 10 and 11. It can be seen from the radiation pattern that the main radiation direction is at an angle to the desired radiation when operating at 7.5GHzHas good consistency. In addition, the corresponding direction of the double light beams isAndIs basically consistent with the design.
The measured far field radiation gains were each 1.5dB less than the analog gains at 7.5GHz frequency due to the limited conductivity of the conductors.
Fig. 12 and 13 are graphs showing the reflection coefficient S11 of the anisotropic holographic impedance super surface according to different operating frequencies. As can be seen from the graph, when the working frequency is in the frequency band of 6.6GHz-8.0GHz, the reflection coefficient of the antenna is smaller than-10 dB, which shows that the bandwidth realizes good impedance matching in the frequency band of 6.6GHz-8.0 GHz.
Although the embodiments of the present invention have been described above with reference to the accompanying drawings, the present invention is not limited to the above-described specific embodiments and application fields, which are merely illustrative, instructive, and not restrictive. Those skilled in the art, having the benefit of this disclosure, may make many forms without departing from the scope of the invention as claimed.
Claims (10)
1. The pure metal anisotropic holographic impedance super-surface antenna is characterized by comprising a transmission array, wherein a monopole antenna is arranged in the center of the transmission array, the transmission array comprises a plurality of impedance units which are arranged in an array manner, each impedance unit comprises a lower metal floor and an upper hollow metal plate, and an air layer is arranged between the two metal plates;
the upper metal plate of each unit consists of a round hollow and a rectangular metal structure penetrating through the hollow center, and an included angle is formed between the upper metal plate and the horizontal plane of the transmission array.
2. A pure metal anisotropic holographic impedance subsurface antenna as in claim 1, wherein said transmissive array comprises 49 x 49 impedance elements.
3. The pure metal anisotropic holographic impedance subsurface antenna of claim 1, wherein the upper layer metal plate has the same thickness as the lower layer metal plate, and the air layer has a thickness that is 2 times the thickness of the upper layer metal plate.
4. The design method of the pure metal anisotropic holographic impedance super-surface antenna is characterized by comprising the following steps of:
Determining the irradiation direction of the wave beam, and acquiring components of impedance tensors of each impedance unit according to the irradiation direction of the wave beam;
Acquiring the relation between the equivalent scalar impedance and the crawling direction of the surface wave according to the components of the impedance tensor of each impedance unit;
Drawing an elliptic curve according to the relation between the equivalent scalar impedance and the crawling direction of the surface wave;
Obtaining the maximum value of equivalent scalar impedance and the included angle between the upper metal plate and the horizontal plane of the transmission array according to the elliptic curve;
and obtaining the radius of the circular hollowed-out part according to the maximum value of the equivalent scalar impedance.
5. The method for designing a pure metal anisotropic holographic impedance super surface antenna according to claim 4, wherein the step of determining the irradiation direction of the beam and obtaining the components of the impedance tensor of each impedance unit according to the irradiation direction of the beam comprises the steps of:
where k z denotes the wave number in the Z-axis direction, k 0 denotes the wave number in free space, Is the normalized equivalent scalar impedance, Z xx,Zxy,Zyy is the three components of the impedance tensor Z, respectively.
6. The method of claim 5, wherein the impedance component is obtained from a surface current field of a monopole antenna on the impedance unit and an electric field of the monopole antenna.
7. The method of claim 5, wherein the component of the impedance tensor Z further comprises Z yx, and the impedance tensor Z is a pure virtual matrix according to the law of conservation of energy and the symmetry characteristics of the proposed element, and Z xy=Zyx.
8. The method for designing a pure metal anisotropic holographic impedance super surface antenna according to claim 4, wherein the drawing of an elliptic curve according to the relationship between the equivalent scalar impedance and the creeping direction of the surface wave is specifically as follows:
And for impedance units at different positions, obtaining a change curve of an equivalent isotropic impedance value of the anisotropic surface impedance along with different crawling angles theta k of the surface wave, wherein the change of the equivalent scalar impedance value of the surface wave in different propagation directions of the tensor impedance surface shows an elliptic curve form.
9. The method for designing a pure metal anisotropic holographic impedance super surface antenna according to claim 4, wherein the maximum value of the equivalent scalar impedance obtained according to the elliptic curve is specifically:
The major axis of the elliptic curve corresponds to the maximum value of the equivalent scalar impedance.
10. The method of claim 4, wherein the angle between the upper metal plate and the horizontal plane of the transmissive array is 90 degrees plus the angle between the long axis of the elliptic curve and the X axis.
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