CN113991318A - Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof - Google Patents

Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof Download PDF

Info

Publication number
CN113991318A
CN113991318A CN202111245769.6A CN202111245769A CN113991318A CN 113991318 A CN113991318 A CN 113991318A CN 202111245769 A CN202111245769 A CN 202111245769A CN 113991318 A CN113991318 A CN 113991318A
Authority
CN
China
Prior art keywords
impedance
wave
holographic
conformal
tensor
Prior art date
Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
Granted
Application number
CN202111245769.6A
Other languages
Chinese (zh)
Other versions
CN113991318B (en
Inventor
李龙
孔旭东
刘海霞
冯强
韩家奇
Current Assignee (The listed assignees may be inaccurate. Google has not performed a legal analysis and makes no representation or warranty as to the accuracy of the list.)
Xidian University
Original Assignee
Xidian University
Priority date (The priority date is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the date listed.)
Filing date
Publication date
Application filed by Xidian University filed Critical Xidian University
Priority to CN202111245769.6A priority Critical patent/CN113991318B/en
Publication of CN113991318A publication Critical patent/CN113991318A/en
Application granted granted Critical
Publication of CN113991318B publication Critical patent/CN113991318B/en
Active legal-status Critical Current
Anticipated expiration legal-status Critical

Links

Images

Classifications

    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F30/00—Computer-aided design [CAD]
    • G06F30/20—Design optimisation, verification or simulation
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/002—Protection against seismic waves, thermal radiation or other disturbances, e.g. nuclear explosion; Arrangements for improving the power handling capability of an antenna
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q1/00—Details of, or arrangements associated with, antennas
    • H01Q1/50—Structural association of antennas with earthing switches, lead-in devices or lightning protectors
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q13/00—Waveguide horns or mouths; Slot antennas; Leaky-waveguide antennas; Equivalent structures causing radiation along the transmission path of a guided wave
    • H01Q13/20—Non-resonant leaky-waveguide or transmission-line antennas; Equivalent structures causing radiation along the transmission path of a guided wave
    • H—ELECTRICITY
    • H01—ELECTRIC ELEMENTS
    • H01Q—ANTENNAS, i.e. RADIO AERIALS
    • H01Q15/00—Devices for reflection, refraction, diffraction or polarisation of waves radiated from an antenna, e.g. quasi-optical devices
    • H01Q15/24—Polarising devices; Polarisation filters 
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F2111/00—Details relating to CAD techniques
    • G06F2111/10—Numerical modelling

Landscapes

  • Engineering & Computer Science (AREA)
  • Physics & Mathematics (AREA)
  • Theoretical Computer Science (AREA)
  • Computer Hardware Design (AREA)
  • Evolutionary Computation (AREA)
  • Geometry (AREA)
  • General Engineering & Computer Science (AREA)
  • General Physics & Mathematics (AREA)
  • Aerials With Secondary Devices (AREA)

Abstract

The invention discloses a conformal surface wave antenna based on a holographic tensor impedance surface and a design method thereof, wherein the design method comprises the following steps: s1: establishing an impedance modulation unit model, and solving eigenfrequency; s2: selecting one slotting angle, changing the side length of the metal patch, the total phase difference of the master boundary and the slave boundary and the transmission direction of the surface wave, and solving equivalent scalar impedance through the eigenfrequency; s3: only changing the side length of the metal patches each time, solving tensor impedance information corresponding to the side length of each group of metal patches, and fitting the relationship between the maximum value of equivalent scalar impedance corresponding to the tensor impedance and the side length of the metal patches; s4: determining a specific expression of each component of tensor impedance; s5: obtaining the side length and the slotting angle of each metal patch based on S3 and S4, and establishing a plane model of the holographic tensor impedance surface; s6: and (3) establishing a conformal curved surface, bending the plane model onto the conformal curved surface, and then adding a feed monopole in the center position of the plane model. The antenna designed by the invention can realize higher aperture efficiency.

Description

Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof
Technical Field
The invention belongs to the technical field of antennas, and particularly relates to a conformal surface wave antenna based on a holographic tensor impedance surface and a design method thereof.
Background
The antenna is an important component in modern wireless communication systems, and is mainly responsible for converting radio frequency signals into spatial electromagnetic waves and radiating the spatial electromagnetic waves, and the performance of the antenna directly affects communication distance and communication quality. The holographic impedance modulation surface antenna based on the artificial electromagnetic surface has the advantages of low profile, small volume, simple feeding and the like, and is easy to attach to the surfaces of various curved surface structures, so that the holographic impedance modulation surface antenna can be conformally designed with a communication system and a protection structure of a flight platform to achieve the aim of structure and function integration.
However, the aperture efficiency of the conventional conformal array antenna is too low, for example, the aperture size of the conformal array antenna based on the scalar impedance surface, which is proposed by a tensile table of electronics and technology, is 243mm by 153mm, the gain of 15dBi can be realized, and the reduced aperture efficiency is only about 4.2%; the conformal scalar impedance surface antenna provided by Zusanya and the like of the university of the Western-An electronic technology has the aperture size of 243mm by 153mm, the gain of 17.08dBi can be realized, and the reduced aperture efficiency is only 6.8%. In order to solve the problem of low aperture efficiency of the conventional conformal array antenna, it is necessary to develop a conformal array antenna with high aperture efficiency and a design method thereof.
Disclosure of Invention
In view of the above-mentioned drawbacks of the prior art, an object of the present invention is to provide a high-gain, high-aperture-efficiency conformal surface wave antenna based on a holographic tensor impedance modulation surface and a method for designing the same.
In order to achieve the purpose, the technical scheme adopted by the invention is as follows: in one aspect, the invention provides a holographic tensor impedance surface-based conformal surface wave antenna, which comprises a conformal holographic tensor impedance surface and a feeding monopole, wherein the feeding monopole is positioned at the center of the conformal holographic tensor impedance surface; the conformal holographic tensor impedance surface modulates the cylindrical surface wave generated by the feed monopole into a plane wave with any direction and any polarization;
the conformal holographic tensor impedance surface is formed by establishing a plane model of the holographic tensor impedance surface and bending the plane model to a conformal curved surface; the plane model of the holographic tensor impedance surface comprises m multiplied by n impedance modulation units which are periodically arranged, and each impedance modulation unit comprises a square metal patch with a slot on the upper layer, a middle-layer medium substrate and a lower-layer square metal floor; the sizes of the square metal patches with slots on the upper layers of the m multiplied by n impedance modulation units are different, and the medium substrate of the middle layer and the square metal floor of the lower layer are all kept to be the same; the square metal patch with the slot is positioned on a central normal of the medium substrate, the slot of the square metal patch with the slot is positioned at the central position of the square metal patch with the slot, the slot length covers the whole square metal patch with the slot, the slot width is equal and is fixed, and the slot angle is selected randomly; the direction in which the maximum value of the equivalent scalar impedance of the impedance modulation unit appears is consistent with the angle of the slot, and the relationship between the maximum value of the equivalent scalar impedance and the square metal patch with the slot is as follows: zmax＝284.6*g4-1155*g3+1713*g2-1125*g1+453.1 wherein ZmaxThe maximum value of equivalent scalar impedance is shown, and g represents the difference between the side length of the square metal patch with the slot and the side length of the square metal floor; selecting the curvature radius of the common curved surface to ensure that the characteristic of the impedance modulation unit after the common curved surface is close to the characteristic of the plane impedance modulation unit;
the impedance distribution of the conformal holographic tensor impedance surface is based on interference fringes of a holographic principle, and all the impedance modulation units are arranged into fringes with different sizes according to a certain mode to simulate the interference fringes;
the interference fringe and impedance distribution based on the holographic principle correspond to a reference wave which is a cylindrical surface wave generated by a feed monopole, and the corresponding target wave is a plane wave with any direction and any polarization, wherein:
reference wave:
Figure BDA0003320803110000021
target wave:
Figure BDA0003320803110000022
Figure BDA0003320803110000023
in the above formulae, JsurfRepresenting a cylindrical surface wave generated by a feed monopole, EradRepresenting plane waves with any direction and any polarization which need to be generated, and modulating the two waves according to the following modes to form tensor surface impedance distribution:
Figure BDA0003320803110000024
Figure BDA0003320803110000025
where X represents the average impedance, M represents the modulation depth,
Figure BDA0003320803110000029
representing the pitch angle and the azimuth angle of an emergent wave beam, x and y representing the plane coordinates of the impedance modulation unit, r representing the radius of the impedance modulation unit on a plane, ρ representing the curvature radius of the conformal curved surface, j representing an imaginary unit, k representing the wave number in free spacetThe wave number of the surface wave is represented,
Figure BDA0003320803110000026
representing the kronecker product of two matrices,
Figure BDA0003320803110000027
the representative taking matrix EradThe conjugate transpose of (a) is performed,
Figure BDA0003320803110000028
the representative fetch matrix JsurfThe conjugate transpose of (1) is a factor for controlling polarization, and is a radiation right-hand circularly polarized wave when p is 1, a radiation left-hand circularly polarized wave when p is-1, and a radiation polarized wave when p is 0.
Further, if m and n are odd numbers, a slotted square metal patch and a part of intermediate layer medium substrate are arranged on the upper layer of an impedance modulation unit at the center position of the impedance surface of the conformal holographic tensor by digging, the size of the intermediate layer medium substrate is determined by the standing-wave ratio of the feeding monopole, and then the feeding monopole is placed in the middle of the hole digging position; if m and n are even numbers, cutting out the upper layers of the four impedance modulation units at the center position of the conformal holographic tensor impedance surface to form a slotted square metal patch and a partial middle layer medium substrate, determining the size of the cut-out middle layer medium substrate through the standing-wave ratio of the feed monopole, and then placing a feed monopole in the middle of the hole cutting position; if m and n are an odd-even, the upper layers of the two impedance modulation units at the center position of the conformal holographic tensor impedance surface are dug to form a slotted square metal patch and a part of the middle-layer medium substrate, the size of the dug middle-layer medium substrate is determined by the standing-wave ratio of the feed monopole, and then the feed monopole is placed in the middle of the dug hole. The reflection coefficient can be adjusted by adjusting the size of the substrate with the middle layer medium excavated so as to complete impedance matching.
Further, m and n are not less than 20. The radiation effect and the leaky wave efficiency can be ensured.
Furthermore, the square metal patch with the slot and the square metal floor are made of pure copper materials, and the thickness of the square metal patch is 35 microns;
preferably, the dielectric substrate is made of a plate with a large dielectric constant, so that a large modulation depth and a large leaky wave efficiency are obtained; more preferably, the dielectric substrate adopts Rogers 3006 with the dielectric constant of 6.15 and the thickness of 1 mm;
preferably, at a target frequency of 10GHz, the side length of the square metal patch with the slot is 2.0mm to 3.3mm, the slot width of the square metal patch with the slot is 0.15mm, and the side length of the square metal floor is 3.4 mm. The numerical values are obtained through software optimization, the numerical values are suitable for the target frequency of 10GHz, and if the working frequency point needs to be replaced, the numerical values need to be re-optimized.
Further, the impedance distribution of the conformal holographic tensor impedance surface is based on interference fringes of a holographic principle, and all the impedance modulation units are arranged into fringes with different sizes according to a certain mode to simulate the interference fringes, specifically: the impedance distribution of the conformal holographic tensor impedance surface is formed by interference superposition of a reference wave radiated by a feed monopole and a target wave of a given wave beam, the conformal design is based on the assumption that the impedance of a plane impedance modulation unit and the impedance of a curved impedance modulation unit are kept consistent, the phase information of the plane wave radiated by the conformal holographic tensor impedance surface is used as the phase of a radiated wave, then the polarization information of the radiated wave is used as the amplitude of the radiated wave, and then the distribution of the impedance modulation unit is used for simulating the interference information of a radiated field and the reference field of the feed monopole, so that an arbitrarily polarized and arbitrarily directed wave beam can be formed when the feed monopole irradiates the conformal holographic tensor impedance surface.
Further, the feeding monopole is a tapered feeding monopole with a large upper part and a small lower part.
Further, the aperture efficiency of the conformal surface wave antenna based on the holographic tensor impedance surface is about 18%.
In another aspect, the present invention provides a method for designing a conformal surface wave antenna based on a holographic tensor impedance surface, which includes the following steps:
s1: establishing an impedance modulation unit model, simulating an infinite periodic array by using a master-slave boundary, and solving eigen frequency by using an eigen mode solver;
s2: randomly selecting one slotting angle of the square metal patch with the slotting on the upper layer, simultaneously changing the side length, the total phase difference of a master-slave boundary and the transmission direction of the surface wave of the square metal patch with the slotting on the upper layer, and solving equivalent scalar impedance through the eigenfrequency calculated in S1;
s3: analyzing the equivalent scalar impedance information obtained by calculation in the step S2, and then knowing that the size of the equivalent scalar impedance is related to the side length of the upper-layer slotted square metal patch and the transmission direction of the surface wave, and cannot be directly solved, so that the relation of the equivalent scalar impedance along with the transmission direction of the surface wave is determined under the condition that the side length of the upper-layer slotted square metal patch is selected, and then each component of anisotropic tensor impedance is solved through a simultaneous equation set; then only changing the side length of the square metal patch with the slot on the upper layer each time, and solving tensor impedance information corresponding to the side length of each group of square metal patches with the slot; finally, fitting a functional relation between the maximum value of equivalent scalar impedance corresponding to tensor impedance and the side length of the square metal patch with the slot on the upper layer according to the obtained tensor impedance information;
s4: determining specific expressions of components of tensor impedance according to a surface impedance theory of the holographic tensor impedance modulation surface antenna and electromagnetic field phase information of the conformal curved surface;
s5: based on the fitting curve relationship obtained in the step S3 and the tensor impedance distribution relationship in the step S4, calculating the side length and the slit angle of the square metal patch with the slit on the upper layer of each impedance modulation unit on the array surface, and establishing a plane model of the holographic tensor impedance surface;
s6: assuming that the refractive index of the square metal patch with the slit is consistent under two conditions of a plane and a micro-curve, a conformal curve is established, the plane model of the holographic tensor impedance surface established in the S5 is bent onto the conformal curve to form the conformal holographic tensor impedance surface, and then the feed monopole is added to the center of the conformal holographic tensor impedance surface to complete the whole design.
Further, the calculation of the equivalent scalar impedance in step S2 is performed according to the following equation:
Figure BDA0003320803110000041
Figure BDA0003320803110000042
wherein Z iseRepresenting equivalent scalar impedance, Z0Which represents the impedance of the wave in free space,
Figure BDA0003320803110000043
and
Figure BDA0003320803110000044
the phase difference in the horizontal and vertical directions on the cross section is shown, c represents the free space light velocity, a represents the side length of the square metal floor, and ω represents the eigenfrequency.
Further, each component of the tensor impedance in step S3 requires three sets of equivalent scalar impedance data of different surface wave transmission directions to be simultaneously connected, and the two sets of equivalent scalar impedance data are transmitted in the same direction
Figure BDA0003320803110000045
Can obtain Zxx、ZyyAnd ZxyWherein
Figure BDA0003320803110000046
Representing an equivalent scalar impedance, obtained by the following equation:
Figure BDA0003320803110000047
wherein eta is0Representing wave impedance in free space, θtRepresents the propagation direction of the surface wave, and j represents an imaginary unit.
Further, the equivalent scalar impedance calculated for the square metal patches with slits of different side lengths in step S3 is a quantity that varies with the transmission direction of the surface wave.
Further, the specific expression of each component of the tensor impedance in the step S4 is obtained by:
the specific expressions of the reference wave and the target wave are as follows:
reference wave:
Figure BDA0003320803110000048
target wave:
Figure BDA0003320803110000049
Figure BDA0003320803110000051
from the holographic tensor impedance modulation formulation,
Figure BDA0003320803110000052
to obtain:
Figure BDA0003320803110000053
Figure BDA0003320803110000054
the specific expression of each component of the tensor impedance is obtained as follows:
Figure BDA0003320803110000055
Figure BDA0003320803110000056
Figure BDA0003320803110000057
Figure BDA0003320803110000058
wherein, JsurfRepresenting a cylindrical surface wave generated by a feed monopole, EradRepresenting any orientation, any, that needs to be generatedPolarized plane waves, X represents the average impedance, M represents the modulation depth,
Figure BDA0003320803110000059
representing the pitch angle and the azimuth angle of an emergent beam, x and y representing the plane coordinates of the impedance modulation unit, r representing the radius of the impedance modulation unit on a plane, ρ representing the curvature radius of the conformal curved surface, j representing an imaginary unit, k0 representing the wave number in free space, ktThe wave number of the surface wave is represented,
Figure BDA00033208031100000510
representing the kronecker product of two matrices,
Figure BDA00033208031100000511
the representative taking matrix EradThe conjugate transpose of (a) is performed,
Figure BDA00033208031100000512
the representative fetch matrix JsurfBeta represents the phase factor after the interference of the outgoing beam and the surface wave, ExAnd EYThe distribution represents the x-direction component and the y-direction component of E, JxAnd JYThe distribution represents the x-direction component and the y-direction component of J,
Figure BDA00033208031100000513
and
Figure BDA00033208031100000514
each represents ExAnd EYThe conjugate transpose of (a) is performed,
Figure BDA00033208031100000515
and
Figure BDA00033208031100000516
each represents JxAnd JYP is a factor for controlling polarization, and is a radiation right-hand circularly polarized wave when p is 1, a radiation left-hand circularly polarized wave when p is-1, and a radiation polarized wave when p is 0.
Compared with the prior art, the invention has the advantages that:
(1) the conformal antenna is designed by adopting the holographic tensor impedance surface (anisotropic tensor impedance modulation unit), the aperture efficiency of the conformal holographic antenna can be effectively improved, compared with the traditional conformal antenna based on the holographic scalar impedance surface, the conformal antenna based on the holographic tensor surface antenna designed by the scheme provided by the invention improves the aperture efficiency to about 18 percent, and can be combined with application scenes such as multi-beam generation, non-diffraction beam generation and the like, so that the multifunctional integration of the conformal curved antenna and the structural function integration of the antenna are realized.
(2) Compared with other units, the unit is convenient to model and process, has a large impedance change range, can realize large modulation depth, and has the advantages of improving the leaky wave efficiency and controlling the caliber size.
(3) The feeding monopole adopted by the invention is a gradually-changed monopole with a large upper part and a small lower part, so that the feeding structure is simple, the working bandwidth of the monopole is increased, the problem that a directional diagram of the monopole is upwarped is solved, and the surface wave is better excited.
Drawings
FIG. 1 is a flow chart of a method of designing a holographic tensor impedance surface based conformal surface wave antenna of the present invention;
FIG. 2 is a schematic diagram of an impedance modulation unit according to the present invention;
fig. 3 (left) is a schematic diagram showing a relationship between a maximum value of the equivalent scalar impedance corresponding to the tensor impedance of the present invention and a size of the square metal patch with the slit, and fig. 3 (right) is a schematic diagram showing a relationship between a slit angle of the present invention and a direction angle of the maximum value of the equivalent scalar impedance corresponding to the tensor impedance;
FIG. 4 is a tensor impedance profile of a (0, 0) degree single beam of the conformal holographic tensor impedance surface of the present invention;
FIG. 5 is a planar model of a holographic tensor impedance surface constructed in accordance with the present invention based on a curve fit relationship and a surface impedance distribution;
FIG. 6 is a schematic overall view of the holographic tensor impedance surface of the present invention after conformality;
FIG. 7 is a simulation model diagram of a feeding monopole of a gradual change version of the present invention;
FIG. 8 is a graph of a (0, 0) degree single beam simulation model of the conformal holographic tensor impedance surface of the present invention;
FIG. 9 (left) is a (0, 0) degree single beam simulated standing wave curve of the conformal holographic tensor impedance surface of the present invention, and FIG. 9 (right) is a (0, 0) degree single beam simulated axial ratio curve of the conformal holographic tensor impedance surface of the present invention;
figure 10 (left) is a (0, 0) degree single beam simulated two-dimensional gain pattern of the conformal holographic tensor impedance surface of the present invention, and figure 10 (right) is a (0, 0) degree single beam simulated three-dimensional gain pattern of the conformal holographic tensor impedance surface of the present invention;
FIG. 11 is a tensor impedance distribution plot of a (30, 45) degree single beam of the conformal holographic tensor impedance surface of the present invention;
FIG. 12 is a graph of a (30, 45) degree single beam simulation model of a conformal holographic tensor impedance surface of the present invention;
fig. 13 (left) is a (30, 45) degree single beam simulated standing wave curve of the conformal holographic tensor impedance surface of the present invention, and fig. 13 (right) is a (30, 45) degree single beam simulated axial ratio curve of the conformal holographic tensor impedance surface of the present invention;
figure 14 (left) is a (30, 45) degree single beam simulated two-dimensional gain pattern of the inventive conformal holographic tensor impedance surface, and figure 14 (right) is a (30, 45) degree single beam simulated three-dimensional gain pattern of the inventive conformal holographic tensor impedance surface;
FIG. 15 is a tensor impedance distribution plot of a (30, 0), (30, 180) degree dual beam of the conformal holographic tensor impedance surface of the present invention;
FIG. 16 is a graph of a (30, 0), (30, 180) degree dual beam simulation model of the conformal holographic tensor impedance surface of the present invention;
FIG. 17 (left) is a standing wave simulation curve for the conformal holographic tensor impedance surface of the present invention (30, 0), (30, 180) degrees dual beams, and FIG. 17 (right) is a standing wave simulation curve for the conformal holographic tensor impedance surface of the present invention (30, 0), (30, 180) degrees dual beams;
figure 18 (left) is a two-beam simulated two-dimensional gain pattern of the inventive conformal holographic tensor impedance surface (30, 0), (30, 180), and figure 18 (right) is a three-dimensional gain pattern of the inventive conformal holographic tensor impedance surface (30, 0), (30, 180).
Detailed Description
The technical solutions of the present invention will be described clearly and completely with reference to the accompanying drawings, and it should be understood that the described embodiments are some, but not all embodiments of the present invention. Other embodiments, which can be derived by one of ordinary skill in the art from the embodiments of the present invention without creative efforts, are within the protection scope of the present invention.
In the description of the present invention, it should be noted that "placing" in the present invention is to be understood in a broad sense, and for example, the placing may be fixedly connected or detachably connected, and the placing may be connected through an intermediate medium or through a circuit, etc. The specific meanings of the above terms in the present invention can be understood in specific cases to those skilled in the art.
Example 1
The working frequency of the conformal holographic tensor impedance surface described in this embodiment is 10GHz, the radius of the conformal cylinder is 219.7mm, the plane size of the whole impedance surface before bending to the conformal curved surface is 153.4mm × 1mm, and the left-handed circularly polarized single beam emitted by the radiation wave with the (0, 0) angle is set, and the specific design process is implemented as follows:
referring to fig. 1, in this embodiment, the whole design is completed step by using the method described in fig. 1, and simulation analysis is performed in the CST, and the result shows that the radiation field has the characteristic of a high-gain single beam, and meets the design requirements, which is specifically described below.
S1: establishing an impedance modulation unit model as shown in fig. 2, wherein the side length of a square metal patch with a slot on the upper layer is in a variable range of 2.0-3.3 mm, the patch is slotted, the slot width is 0.15mm, the slot angle can be changed, the side length of a square metal floor on the lower layer is 3.4mm, the thickness of a medium substrate in the middle is 1mm, and the material is Rogers 3006; simulating an infinite periodic array by using a master-slave boundary, neglecting refractive index errors caused by size change, and solving eigenfrequency by using an eigenmode solver;
s2: selecting a slotting angle of 45 degrees, setting the total phase difference of a master boundary and a slave boundary to be 30-180 degrees, setting the side length change range of a square metal patch with the slotting to be 2.0-3.3 mm, setting the transmission direction of a surface wave to be 0-170 degrees, and solving equivalent scalar impedance through the intrinsic frequency obtained through calculation;
s3: analyzing the equivalent scalar impedance information obtained by calculation in the step S2, and then knowing that the size of the equivalent scalar impedance is related to the side length of the upper-layer slotted square metal patch and the transmission direction of the surface wave, and cannot be directly solved, so that the relation of the equivalent scalar impedance along with the transmission direction of the surface wave is determined under the condition that the side length of the upper-layer slotted square metal patch is selected, and then each component of anisotropic tensor impedance is solved through a simultaneous equation set; then, selecting the side length of a square metal patch with a slot each time, then obtaining the side length of each group of square metal patches with slots and tensor impedance information corresponding to data in the transmission direction, and fitting the relationship between the maximum value of equivalent scalar impedance corresponding to the tensor impedance and the side length of the square metal patch with the slot, wherein the fitting formula is as follows: zmax＝284.6*g4-1155*g3+1713*g2-1125*g1+453.1 wherein ZmaxRepresenting the maximum value of equivalent scalar impedance, g representing the difference between the side lengths of the upper layer square metal patch with the slot and the lower layer square metal floor, and drawing the relation in a rectangular coordinate system, as shown in fig. 3 (left); by analyzing the relationship between the slit angle and the direction angle of the maximum value of the equivalent scalar impedance corresponding to the tensor impedance, as shown in fig. 3 (right), it is considered that the slit angle can control the position where the maximum finger of the equivalent scalar impedance appears;
s4: to determine the specific expressions for the components of the tensor impedance, specific expressions for the left-handed circularly polarized radiation field and the reference wave need to be given:
reference wave:
Figure BDA0003320803110000081
radiation field:
Figure BDA0003320803110000082
Figure BDA0003320803110000083
from the holographic tensor impedance modulation formulation,
Figure BDA0003320803110000084
to obtain:
Figure BDA0003320803110000085
Figure BDA0003320803110000086
the expression for each component is then:
Figure BDA0003320803110000087
Figure BDA0003320803110000088
Figure BDA0003320803110000089
Figure BDA00033208031100000810
according to the above respective formulas, and bringing into the setting conditions of example 1
Figure BDA00033208031100000811
p-1, p-219.4 mm, and an array size of 153.4mm, the tensor impedance distribution was calculated as shown in figure 4.
S5: from the above calculation and the fitting analysis in S3, the size of each impedance modulation element on the wavefront and the slit angle are calculated, and a planar model of the entire holographic tensor impedance surface is created, as shown in fig. 5.
S6: a conformal curved surface is established, the plane model of the holographic tensor impedance surface established in S5 is bent onto the curved surface to be conformal, so as to form the conformal holographic tensor impedance surface, and then the feeding monopole is added to the center of the conformal holographic tensor impedance surface, so as to complete the whole design, as shown in fig. 6. In order to solve the problem of upward warping of the directional diagram of the traditional monopole, the feeding monopole with the curved surface adopts a gradual-change structure with a large upper part and a small lower part, so that the surface wave can be excited better, and a simulation model of the feeding monopole is shown in fig. 7.
Completing the above process, and completing the design of the conformal holographic tensor impedance surface pointed by the established wave beam, wherein in order to verify the working performance of the designed conformal antenna, full-wave simulation is required to be performed, and the standing wave characteristic and the directional diagram characteristic of the antenna are analyzed; the designed conformal holographic impedance surface antenna is simulated by CST software, a simulated modeling graph is shown in figure 8, a simulated standing wave curve is shown in figure 9 (left), and the result shows that in a set frequency band, all reflection coefficients are lower than-8 dB, the relative impedance bandwidth is more than 20%, the reflection coefficient at a working frequency band of 10GHz is lower than-10 dB, and the matching effect is good; the simulated axial ratio curve is shown in fig. 9 (right), and the result shows that the axial ratio in the main beam direction is lower than 3dB, and the circular polarization effect is good; as shown in fig. 10, it can be seen that a gain of 17.7dBi can be achieved, the level of the side lobe is-12.5 dB, and the reduced aperture efficiency is 17.9% (the data for calculating the aperture efficiency is derived from the following calculation formula:
Figure BDA0003320803110000091
wherein G is0Denotes the absolute gain, ApThe aperture of the array is represented, and lambda represents the wavelength of the working frequency band), the beam direction is (0, 0) degree, the radiation effect is good, the aperture efficiency is high, and the design requirements are met.
Example 2
The working frequency of the conformal holographic tensor impedance surface described in this embodiment is 10GHz, the radius of the conformal cylinder is set to be 244mm, the plane size before the whole holographic impedance surface is conformal is 153.4mm by 1mm, and the radiation wave is set to be a right-hand circularly polarized single beam emitted at an angle of (30, 45), and the specific design process is implemented as follows:
referring to fig. 1, in this embodiment, the method described in fig. 1 is used to complete the whole design, and simulation analysis is performed in the CST, and the result shows that the radiation field has the characteristic of a high-gain single beam, which meets the design requirements, and the following description specifically illustrates:
s1: establishing an impedance modulation unit model as shown in fig. 2, wherein the side length of a square metal patch with a slot on the upper layer is in a variable range of 2.0-3.3 mm, the patch is slotted, the slot width is 0.15mm, the slot angle can be changed, the side length of a square metal floor on the lower layer is 3.4mm, the thickness of a medium substrate in the middle is 1mm, and the material is Rogers 3006; simulating an infinite periodic array by using a master-slave boundary, neglecting refractive index errors caused by size change, and solving eigenfrequency by using an eigenmode solver;
s2: selecting a slotting angle of 45 degrees, setting the total phase difference of a master boundary and a slave boundary to be 30-180 degrees, setting the side length change range of a square metal patch with the slotting to be 2.0-3.3 mm, setting the transmission direction of a surface wave to be 0-170 degrees, and solving equivalent scalar impedance through the intrinsic frequency obtained through calculation;
s3: analyzing the equivalent scalar impedance information obtained by calculation in the step S2, and then knowing that the size of the equivalent scalar impedance is related to the side length of the upper-layer slotted square metal patch and the transmission direction of the surface wave, and cannot be directly solved, so that the relation of the equivalent scalar impedance along with the transmission direction of the surface wave is determined under the condition that the side length of the upper-layer slotted square metal patch is selected, and then each component of anisotropic tensor impedance is solved through a simultaneous equation set; then, selecting the side length of a square metal patch with a slot each time, then obtaining the side length of each group of square metal patches with the slot and tensor impedance information corresponding to the data of the transmission direction, and fitting the maximum value of equivalent scalar impedance corresponding to the tensor impedance and the square metal with the slotBelongs to the relation between the side lengths of the patches, and the fitting formula is as follows: zmax＝284.6*g4-1155*g3+1713*g2-1125*g1+453.1 wherein ZmaxRepresenting the maximum value of equivalent scalar impedance, g representing the difference between the side lengths of the upper layer square metal patch with the slot and the lower layer square metal floor, and drawing the relation in a rectangular coordinate system, as shown in fig. 3 (left); by analyzing the relationship between the slit angle and the direction angle of the maximum value of the equivalent scalar impedance corresponding to the tensor impedance, as shown in fig. 3 (right), it is considered that the slit angle can control the position where the maximum finger of the equivalent scalar impedance appears;
s4: in order to determine the specific expressions of the components of the tensor impedance, specific expressions of the right-hand circularly polarized radiation field and the reference wave need to be given:
reference wave:
Figure BDA0003320803110000101
radiation field:
Figure BDA0003320803110000102
Figure BDA0003320803110000103
from the holographic tensor impedance modulation formulation,
Figure BDA0003320803110000104
to obtain:
Figure BDA0003320803110000105
Figure BDA0003320803110000106
the expression for each component is then:
Figure BDA0003320803110000107
Figure BDA0003320803110000108
Figure BDA0003320803110000109
Figure BDA00033208031100001010
according to the above respective formulas, and bringing into the setting conditions of example 2
Figure BDA00033208031100001011
p +1, p 244mm, array size 153.4mm, and the calculated tensor impedance distribution is shown in fig. 11.
S5: according to the above calculation and the fitting analysis in step S3, the size of each impedance modulation element on the wavefront and the slit angle are calculated, and a planar model of the entire holographic tensor impedance surface is created.
S6: and (3) establishing a conformal curved surface, bending the plane model of the holographic tensor impedance surface established in the step (S5) onto the curved surface to be conformal to form the conformal holographic tensor impedance surface, and adding a feed monopole into the center of the conformal holographic tensor impedance surface to complete the whole design. The curved-surface feed monopole with the gradual-change structure of the embodiment 1 is still adopted, so that the surface wave can be excited better.
In order to verify the working performance of the designed conformal antenna, full-wave simulation is required, and CST software is used for analyzing the standing wave characteristic and the far-field characteristic of the antenna; the simulated modeling graph is shown in fig. 12, the simulated standing wave curve is shown in fig. 13 (left), and the result shows that in the set frequency band, the reflection coefficients are all lower than-10 dB, the relative impedance bandwidth is more than 20%, the reflection coefficient at the working frequency band of 10GHz is lower than-15.8 dB, and the matching effect is good; the simulated axial ratio curve is shown in fig. 13 (right), and the result shows that the axial ratio is lower than 4dB in the main beam direction; the two-dimensional gain directional diagram and the three-dimensional gain directional diagram are shown in fig. 14, and it can be seen that the gain of 16.8dBi can be realized, the level of the side lobe is-7.6 dB, the reduced aperture efficiency is 16%, the beam direction is (32, 50) degrees, the beam direction is slightly offset, the radiation effect is good, the aperture efficiency is high, and the design requirements are met.
Example 3
The working frequency of the conformal holographic tensor impedance surface described in this embodiment is 10GHz, the radius of the conformal cylinder is set to be 244mm, the plane size before the whole holographic impedance surface is conformal is 153.4mm by 1mm, and the radiation waves are set to be circularly polarized symmetric dual beams with opposite rotation directions emitted at angles of (30, 0) and (30, 180), and the specific design flow is implemented as follows:
referring to fig. 1, in this embodiment, the method described in fig. 1 is used to complete the whole design, and simulation analysis is performed in the CST, and the result shows that the radiation field has the characteristic of a high-gain single beam, which meets the design requirements, and the following description specifically illustrates:
s1: establishing an impedance modulation unit model as shown in fig. 2, wherein the side length of a square metal patch with a slot on the upper layer is in a variable range of 2.0-3.3 mm, the patch is slotted, the slot width is 0.15mm, the slot angle can be changed, the side length of a square metal floor on the lower layer is 3.4mm, the thickness of a medium substrate in the middle is 1mm, and the material is Rogers 3006; simulating an infinite periodic array by using a master-slave boundary, neglecting refractive index errors caused by size change, and solving eigenfrequency by using an eigenmode solver;
s2: selecting a slotting angle of 45 degrees, setting the total phase difference of a master boundary and a slave boundary to be 30-180 degrees, setting the side length change range of a square metal patch with the slotting to be 2.0-3.3 mm, setting the transmission direction of a surface wave to be 0-170 degrees, and solving equivalent scalar impedance through the intrinsic frequency obtained through calculation;
s3: after analyzing the equivalent scalar impedance information calculated in S2, it is known that the size of the equivalent scalar impedance is related to the side length of the upper-layer square metal patch with the slit and the transmission direction of the surface wave, and cannot be directly solved, so that the equivalent scalar impedance is determined first when the side length of the upper-layer square metal patch with the slit is selectedMeasuring the relation of impedance along with the transmission direction of the surface wave, and then solving each component of anisotropic tensor impedance through a simultaneous equation set; then, selecting the side length of a square metal patch with a slot each time, then obtaining the side length of each group of square metal patches with slots and tensor impedance information corresponding to data in the transmission direction, and fitting the relationship between the maximum value of equivalent scalar impedance corresponding to the tensor impedance and the side length of the square metal patch with the slot, wherein the fitting formula is as follows: zmax＝284.6*g4-1155*g3+1713*g2-1125*g1+453.1 wherein ZmaxRepresenting the maximum value of equivalent scalar impedance, g representing the difference between the side lengths of the upper layer square metal patch with the slot and the lower layer square metal floor, and drawing the relation in a rectangular coordinate system, as shown in fig. 3 (left); by analyzing the relationship between the slit angle and the direction angle of the maximum value of the equivalent scalar impedance corresponding to the tensor impedance, as shown in fig. 3 (right), it is considered that the slit angle can control the position where the maximum finger of the equivalent scalar impedance appears;
s4: in order to determine the specific expressions of the components of the tensor impedance, specific expressions of the circularly polarized radiation field and the reference wave of the symmetrical dual beams with different handedness need to be given:
reference wave:
Figure BDA0003320803110000121
radiation field:
Figure BDA0003320803110000122
Figure BDA0003320803110000123
Figure BDA0003320803110000124
Figure BDA0003320803110000125
from the holographic tensor impedance modulation formulation,
Figure BDA0003320803110000126
we have found that:
Figure BDA0003320803110000127
Figure BDA0003320803110000128
the expression for each component is then:
Figure BDA0003320803110000129
Figure BDA00033208031100001210
Figure BDA00033208031100001211
Figure BDA00033208031100001212
Figure BDA00033208031100001213
according to the above respective formulas, and bringing into the setting conditions of example 3
Figure BDA00033208031100001214
Figure BDA00033208031100001215
ρ 244mm, array size 153.4mm, and the calculated tensor impedance distribution is shown in fig. 15.
S5: according to the above calculation and the fitting analysis in step S3, the size of each impedance modulation element on the wavefront and the slit angle are calculated, and a planar model of the entire holographic tensor impedance surface is created.
S6: a conformal curved surface is established, the plane model of the holographic tensor impedance surface established in S5 is bent onto the curved surface to be conformal, so as to form a conformal holographic tensor impedance surface, and then a feeding monopole is added to the center of the conformal holographic tensor impedance surface, so as to complete the whole design, as shown in fig. 16. The curved-surface feed monopole with the gradual-change structure of the embodiment 1 is still adopted, so that the surface wave can be excited better.
In order to verify the working performance of the designed conformal antenna, full-wave simulation is required to be carried out, and the standing wave characteristic and the directional pattern characteristic of the antenna are analyzed; the designed conformal holographic impedance surface antenna is simulated by CST software, a simulated standing wave curve is shown in figure 17 (left), and the result shows that all reflection coefficients are lower than-7.5 dB in a set frequency band, the reflection coefficient at a working frequency band of 10GHz is lower than-10 dB, and the matching effect is good; the simulated axial ratio curve is shown in fig. 17 (right), and the result shows that the axial ratio is lower than 3dB in the direction of the double main beams, and the circular polarization effect is good; the two-dimensional gain directional diagram and the three-dimensional gain directional diagram are shown in fig. 18, and it can be seen that symmetric dual-beam radiation is realized, the radiation directions are (30, 0) and (30, 180), respectively, the gain of each beam is 14.9dB, the sidelobe level is-8.4 dB, and the radiation effect is good; the caliber efficiency is 18.7 percent, and the design requirement is met.
In conclusion, the invention realizes the high-efficiency conformal antenna based on the holographic tensor impedance modulation surface, cylindrical waves generated by the gradient monopole feed source are changed into any established wave beams through the modulation of the impedance surface and are radiated out, and high-gain directional wave beams are formed in the radiation direction.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and those skilled in the art can make various changes and modifications without departing from the inventive concept of the present invention, but all such changes and modifications fall within the scope of the present invention.

Claims (10)

1. A conformal surface wave antenna based on a holographic tensor impedance surface comprises the conformal holographic tensor impedance surface and a feeding monopole, wherein the feeding monopole is positioned in the center of the conformal holographic tensor impedance surface; the conformal holographic tensor impedance surface modulates the cylindrical surface wave generated by the feed monopole into a plane wave with any direction and any polarization;
the conformal holographic tensor impedance surface is formed by establishing a plane model of the holographic tensor impedance surface and bending the plane model to a conformal curved surface; the plane model of the holographic tensor impedance surface comprises m multiplied by n impedance modulation units which are periodically arranged, and each impedance modulation unit comprises a square metal patch with a slot on the upper layer, a middle-layer medium substrate and a lower-layer square metal floor; the sizes of the square metal patches with slots on the upper layers of the m multiplied by n impedance modulation units are different, and the medium substrate of the middle layer and the square metal floor of the lower layer are all kept to be the same; the square metal patch with the slot is positioned on a central normal of the medium substrate, the slot of the square metal patch with the slot is positioned at the central position of the square metal patch with the slot, the length of the slot covers the whole square metal patch with the slot, the width of the slot is a fixed value, and the slot angle is selected at will; the direction in which the maximum value of the equivalent scalar impedance of the impedance modulation unit appears is consistent with the angle of the slot, and the relationship between the maximum value of the equivalent scalar impedance and the square metal patch with the slot is as follows: zmax＝284.6*g4-1155*g3+1713*g2-1125*g1+453.1 wherein ZmaxThe maximum value of equivalent scalar impedance is shown, and g represents the difference between the side length of the square metal patch with the slot and the side length of the square metal floor; selecting the curvature radius of the common curved surface to ensure that the characteristic of the impedance modulation unit after the common curved surface is close to the characteristic of the plane impedance modulation unit;
the impedance distribution of the conformal holographic tensor impedance surface is based on interference fringes of a holographic principle, and all the impedance modulation units are arranged into fringes with different sizes according to a certain mode to simulate the interference fringes;
the interference fringe and impedance distribution based on the holographic principle correspond to a reference wave which is a cylindrical surface wave generated by a feed monopole, and the corresponding target wave is a plane wave with any direction and any polarization, wherein:
reference wave:
Figure FDA0003320803100000011
target wave:
Figure FDA0003320803100000012
Figure FDA0003320803100000013
in the above formulae, JsurfRepresenting a cylindrical surface wave generated by a feed monopole, EradRepresenting plane waves with any direction and any polarization which need to be generated, and modulating the two waves according to the following modes to form tensor surface impedance distribution:
Figure FDA0003320803100000014
Figure FDA0003320803100000015
where X represents the average impedance, M represents the modulation depth, (theta,
Figure FDA0003320803100000016
) Representing the pitch angle and the azimuth angle of an emergent wave beam, x and y representing the plane coordinates of the impedance modulation unit, r representing the radius of the impedance modulation unit on a plane, ρ representing the curvature radius of the conformal curved surface, j representing an imaginary unit, k representing the wave number in free spacetThe wave number of the surface wave is represented,
Figure FDA0003320803100000017
representing the kronecker product of two matrices,
Figure FDA0003320803100000018
the representative taking matrix EradThe conjugate transpose of (a) is performed,
Figure FDA0003320803100000019
the representative fetch matrix JsurfThe conjugate transpose of (1) is a factor for controlling polarization, and is a radiation right-hand circularly polarized wave when p is 1, a radiation left-hand circularly polarized wave when p is-1, and a radiation polarized wave when p is 0.
2. The conformal surface wave antenna based on the holographic tensor impedance surface as recited in claim 1, wherein if m and n are odd numbers, a slotted square metal patch and a part of the middle layer medium substrate are arranged on an upper layer of an impedance modulation unit which is dug out of the center position of the conformal holographic tensor impedance surface, the size of the middle layer medium substrate is determined by the standing-wave ratio of the feeding monopole, and then the feeding monopole is placed in the middle of the dug-out position; if m and n are even numbers, cutting out the upper layers of the four impedance modulation units at the center position of the conformal holographic tensor impedance surface to form a slotted square metal patch and a partial middle layer medium substrate, determining the size of the cut-out middle layer medium substrate through the standing-wave ratio of the feed monopole, and then placing a feed monopole in the middle of the hole cutting position; if m and n are an odd-even, the upper layers of the two impedance modulation units at the center position of the conformal holographic tensor impedance surface are dug to form a slotted square metal patch and a part of the middle-layer medium substrate, the size of the dug middle-layer medium substrate is determined by the standing-wave ratio of the feed monopole, and then the feed monopole is placed in the middle of the dug hole.
3. The holographic tensor impedance surface-based conformal surface wave antenna of claim 1, wherein m and n are not less than 20.
4. The holographic tensor impedance surface-based conformal surface wave antenna of claim 1, wherein the slotted square metal patch and square metal floor are of pure copper material and have a thickness of 35 microns;
preferably, the dielectric substrate is made of a plate with a large dielectric constant, so that a large modulation depth and a large leaky wave efficiency are obtained; more preferably, the dielectric substrate adopts Rogers 3006 with the dielectric constant of 6.15 and the thickness of 1 mm;
preferably, at a target frequency of 10GHz, the side length of the square metal patch with the slot is 2.0mm to 3.3mm, the slot width of the square metal patch with the slot is 0.15mm, and the side length of the square metal floor is 3.4 mm.
5. The conformal surface wave antenna based on the holographic tensor impedance surface of claim 1, wherein an impedance distribution of the conformal holographic tensor impedance surface is based on interference fringes of a holographic principle, and all the impedance modulation units are arranged into fringes with different sizes according to a certain mode to simulate the interference fringes, and specifically: the impedance distribution of the conformal holographic tensor impedance surface is formed by interference superposition of a reference wave radiated by a feed monopole and a target wave of a given wave beam, the conformal design is based on the assumption that the impedance of a plane impedance modulation unit and the impedance of a curved impedance modulation unit are kept consistent, the phase information of the plane wave radiated by the conformal holographic tensor impedance surface is used as the phase of a radiated wave, then the polarization information of the radiated wave is used as the amplitude of the radiated wave, and then the distribution of the impedance modulation unit is used for simulating the interference information of a radiated field and the reference field of the feed monopole, so that an arbitrarily polarized and arbitrarily directed wave beam can be formed when the feed monopole irradiates the conformal holographic tensor impedance surface.
6. The holographic tensor impedance surface based conformal surface wave antenna of any one of claims 1-5, wherein the feed monopole is a tapered feed monopole that is large at the top and small at the bottom.
7. The method of designing a holographic tensor impedance surface based conformal surface wave antenna of any one of claims 1-6, comprising the steps of:
s1: establishing an impedance modulation unit model, simulating an infinite periodic array by using a master-slave boundary, and solving eigen frequency by using an eigen mode solver;
s2: randomly selecting one slotting angle of the square metal patch with the slotting on the upper layer, simultaneously changing the side length, the total phase difference of a master-slave boundary and the transmission direction of the surface wave of the square metal patch with the slotting on the upper layer, and solving equivalent scalar impedance through the eigenfrequency calculated in S1;
s3: analyzing the equivalent scalar impedance information obtained by calculation in the step S2, and then knowing that the size of the equivalent scalar impedance is related to the side length of the upper-layer slotted square metal patch and the transmission direction of the surface wave, and cannot be directly solved, so that the relation of the equivalent scalar impedance along with the transmission direction of the surface wave is determined under the condition that the side length of the upper-layer slotted square metal patch is selected, and then each component of anisotropic tensor impedance is solved through a simultaneous equation set; then only changing the side length of the square metal patch with the slot on the upper layer each time, and solving tensor impedance information corresponding to the side length of each group of square metal patches with the slot; finally, fitting a functional relation between the maximum value of equivalent scalar impedance corresponding to tensor impedance and the side length of the square metal patch with the slot on the upper layer according to the obtained tensor impedance information;
s4: determining specific expressions of components of tensor impedance according to a surface impedance theory of the holographic tensor impedance modulation surface antenna and electromagnetic field phase information of the conformal curved surface;
s5: based on the fitting curve relationship obtained in the step S3 and the tensor impedance distribution relationship in the step S4, calculating the side length and the slit angle of the square metal patch with the slit on the upper layer of each impedance modulation unit on the array surface, and establishing a plane model of the holographic tensor impedance surface;
s6: assuming that the refractive index of the square metal patch with the slit is consistent under two conditions of a plane and a micro-curve, a conformal curve is established, the plane model of the holographic tensor impedance surface established in the S5 is bent onto the conformal curve to form the conformal holographic tensor impedance surface, and then the feed monopole is added to the center of the conformal holographic tensor impedance surface to complete the whole design.
8. The design method according to claim 7, wherein the calculation of the equivalent scalar impedance in step S2 is performed according to the following equation:
Figure FDA0003320803100000031
wherein Z iseRepresenting equivalent scalar impedance, Z0Which represents the impedance of the wave in free space,
Figure FDA0003320803100000032
and
Figure FDA0003320803100000033
the phase difference in the horizontal and vertical directions on the cross section is shown, c represents the free space light velocity, a represents the side length of the square metal floor, and ω represents the eigenfrequency.
9. The method of claim 7, wherein each component of the tensor impedance in step S3 requires three sets of equivalent scalar impedance data for different surface wave propagation directions in parallel, and wherein
Figure FDA0003320803100000034
Can obtain Zxx、ZyyAnd ZxyWherein
Figure FDA0003320803100000035
Representing an equivalent scalar impedance, obtained by the following equation:
Figure FDA0003320803100000041
wherein eta is0Representing wave impedance in free space, θtRepresents the propagation direction of the surface wave, and j represents an imaginary unit.
10. The design method according to claim 7, wherein the specific expression of each component of the tensor impedance in step S4 is obtained by:
the specific expressions of the reference wave and the target wave are as follows:
reference wave:
Figure FDA0003320803100000042
target wave:
Figure FDA0003320803100000043
Figure FDA0003320803100000044
from the holographic tensor impedance modulation formulation,
Figure FDA0003320803100000045
to obtain:
Figure FDA0003320803100000046
Figure FDA0003320803100000047
the specific expression of each component of the tensor impedance is obtained as follows:
Figure FDA0003320803100000048
Figure FDA0003320803100000049
Figure FDA00033208031000000410
Figure FDA00033208031000000411
wherein, JsurfRepresenting a cylindrical surface wave generated by a feed monopole, EradRepresenting an arbitrarily directed, arbitrarily polarized plane wave that needs to be generated, X representing the average impedance, M representing the modulation depth, (theta,
Figure FDA00033208031000000412
) Representing the pitch angle and the azimuth angle of an emergent beam, x and y representing the plane coordinates of the impedance modulation unit, r representing the radius of the impedance modulation unit on a plane, ρ representing the curvature radius of the conformal curved surface, j representing an imaginary unit, k0 representing the wave number in free space, ktThe wave number of the surface wave is represented,
Figure FDA00033208031000000413
representing the kronecker product of two matrices,
Figure FDA00033208031000000414
the representative taking matrix EradThe conjugate transpose of (a) is performed,
Figure FDA00033208031000000415
the representative fetch matrix JsurfBeta represents the phase factor after the interference of the outgoing beam and the surface wave, ExAnd EYThe distribution represents the x-direction component and the y-direction component of E, JxAnd JYThe distribution represents the x-direction component and the y-direction component of J,
Figure FDA00033208031000000416
and
Figure FDA00033208031000000417
each represents ExAnd EYThe conjugate transpose of (a) is performed,
Figure FDA00033208031000000418
and
Figure FDA00033208031000000419
each represents JxAnd JYP is a factor for controlling polarization, and is a radiation right-hand circularly polarized wave when p is 1, a radiation left-hand circularly polarized wave when p is-1, and a radiation polarized wave when p is 0.
CN202111245769.6A 2021-10-26 2021-10-26 Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof Active CN113991318B (en)

Priority Applications (1)

Application Number Priority Date Filing Date Title
CN202111245769.6A CN113991318B (en) 2021-10-26 2021-10-26 Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof

Applications Claiming Priority (1)

Application Number Priority Date Filing Date Title
CN202111245769.6A CN113991318B (en) 2021-10-26 2021-10-26 Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof

Publications (2)

Publication Number Publication Date
CN113991318A true CN113991318A (en) 2022-01-28
CN113991318B CN113991318B (en) 2023-01-20

Family

ID=79741378

Family Applications (1)

Application Number Title Priority Date Filing Date
CN202111245769.6A Active CN113991318B (en) 2021-10-26 2021-10-26 Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof

Country Status (1)

Country Link
CN (1) CN113991318B (en)

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114465013A (en) * 2022-02-21 2022-05-10 西安电子科技大学 Spherical conformal dual-circular-polarization dual-beam antenna based on anisotropic holographic super surface

Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7911407B1 (en) * 2008-06-12 2011-03-22 Hrl Laboratories, Llc Method for designing artificial surface impedance structures characterized by an impedance tensor with complex components
CN104733850A (en) * 2015-04-17 2015-06-24 电子科技大学 Holographic modulation based artificial tensor impedance surfaced antenna and implementation method thereof
CN107086350A (en) * 2016-02-16 2017-08-22 通用汽车环球科技运作有限责任公司 For mitigating surface wave and improving the impedance surface treating part of glass antenna gain
CN107394408A (en) * 2017-07-24 2017-11-24 电子科技大学 Vortex electromagnetic beam antenna and its implementation based on holographic tensor impedance surface
CN110011069A (en) * 2019-04-15 2019-07-12 西安电子科技大学 Shaped surfaces wave antenna based on holographic super surface
US20190245263A1 (en) * 2018-02-06 2019-08-08 Hrl Laboratories, Llc Interleaved array of antennas operable at multiple frequencies
US10454179B1 (en) * 2016-08-10 2019-10-22 Hrl Laboratories, Llc Holographic artificial impedance antennas with flat lens feed structure
CN111864375A (en) * 2020-07-21 2020-10-30 河北工业大学 Compact one-dimensional holographic electromagnetic metasurface antenna

Patent Citations (8)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
US7911407B1 (en) * 2008-06-12 2011-03-22 Hrl Laboratories, Llc Method for designing artificial surface impedance structures characterized by an impedance tensor with complex components
CN104733850A (en) * 2015-04-17 2015-06-24 电子科技大学 Holographic modulation based artificial tensor impedance surfaced antenna and implementation method thereof
CN107086350A (en) * 2016-02-16 2017-08-22 通用汽车环球科技运作有限责任公司 For mitigating surface wave and improving the impedance surface treating part of glass antenna gain
US10454179B1 (en) * 2016-08-10 2019-10-22 Hrl Laboratories, Llc Holographic artificial impedance antennas with flat lens feed structure
CN107394408A (en) * 2017-07-24 2017-11-24 电子科技大学 Vortex electromagnetic beam antenna and its implementation based on holographic tensor impedance surface
US20190245263A1 (en) * 2018-02-06 2019-08-08 Hrl Laboratories, Llc Interleaved array of antennas operable at multiple frequencies
CN110011069A (en) * 2019-04-15 2019-07-12 西安电子科技大学 Shaped surfaces wave antenna based on holographic super surface
CN111864375A (en) * 2020-07-21 2020-10-30 河北工业大学 Compact one-dimensional holographic electromagnetic metasurface antenna

Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114465013A (en) * 2022-02-21 2022-05-10 西安电子科技大学 Spherical conformal dual-circular-polarization dual-beam antenna based on anisotropic holographic super surface

Also Published As

Publication number Publication date
CN113991318B (en) 2023-01-20

Similar Documents

Publication Publication Date Title
CN203644950U (en) Compact field antenna based on flat reflective array
Giddens et al. Multibeam graded dielectric lens antenna from multimaterial 3-D printing
CN110011069B (en) Conformal surface wave antenna based on holographic super surface
CN113708077A (en) Beam forming super-surface structure and method based on amplitude and phase modulation
CN105514622A (en) Four-frequency microstrip reflective array antenna
CN113991318B (en) Conformal surface wave antenna based on holographic tensor impedance surface and design method thereof
CN110729821B (en) Quasi-diffraction-free beam forming method for multi-target wireless energy transmission
Li et al. Reflectarray element using interdigital gap loading structure
CN113328242B (en) High-preparation-property eight-diagram-type element metamaterial cladding microstrip antenna and design method thereof
Suárez et al. Experimental validation of linear aperiodic array for grating lobe suppression
CN115051168B (en) Single-layer flat plate ultra-wideband ultra-surface lens and lens antenna
CN117039412A (en) Broadband reflection array antenna using Archimedes and sine wave mixed curve
CN108682968B (en) Single-feed three-beam low-RCS super-surface included angle reflector antenna
US10396462B2 (en) C-band conformal antenna using microstrip circular patches and methods thereof
Rana et al. Design, simulation, and analysis of microstrip patch antenna for wireless applications operating at 3.6 GHz
Kumar et al. Dual-band flat-top pattern synthesis using phase gradient metasurface
CN102810755B (en) Metamaterial antenna
CN114883773A (en) Antenna structure, electronic equipment and wireless network system
Mahmoodi et al. Enhancement of scan angle using a Rotman lens feeding network for a conformal array antenna configuration
Kadyrova et al. Microstrip patch antenna with band rejection design for V2X technology based on 5G networks
CN112736483A (en) Polarization reconfigurable two-dimensional beam scanning holographic antenna and implementation method thereof
Kavitha et al. An analytical approach for design of Microstrip Patch (MSP)
CN114465013B (en) Spherical conformal dual-circularly polarized dual-beam antenna based on anisotropic holographic super surface
CN114899621B (en) Decoupling circular polarization four-vortex beam antenna and design method
Ahmed et al. Design of a Compact Transparent Antenna for 5GWireless Applications

Legal Events

Date Code Title Description
PB01 Publication
PB01 Publication
SE01 Entry into force of request for substantive examination
SE01 Entry into force of request for substantive examination
GR01 Patent grant
GR01 Patent grant