CN113991318B - 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 PDFInfo
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
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- H—ELECTRICITY
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- H01Q1/50—Structural association of antennas with earthing switches, lead-in devices or lightning protectors
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- 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
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
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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
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 provided by a tensile table of electronics science 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 Zhang Jingya, et al, of the university of Western An electronic technology has an aperture size of 243mm 153mm, can achieve a gain of 17.08dBi, and has a reduced aperture efficiency of 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 realize the purpose, the technical scheme adopted by the invention is as follows: in one aspect, the invention provides a conformal surface wave antenna based on a holographic tensor impedance surface, which comprises the 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; said belt isThe slotted square metal patch is positioned on the central normal of the medium substrate, the slot of the slotted square metal patch is positioned at the central position of the slotted square metal patch, the slot length covers the whole slotted square metal patch, 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: z max ＝284.6*g 4 -1155*g 3 +1713*g 2 -1125*g 1 +453.1 wherein Z max The maximum value of equivalent scalar impedance is represented, g represents the difference of the side length of the square metal patch with the slot and the square metal floor; selecting the curvature radius of the conformal curved surface to ensure that the characteristic of the impedance modulation unit after conformal is close to the characteristic of a 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:
target wave:
in the above formulae, J surf Representing a cylindrical surface wave generated by a feed monopole, E rad Representing any direction, task, etc. that needs to be generatedThe intentionally polarized plane wave is modulated by the two waves in the following way to form tensor surface impedance distribution:
where X represents the average impedance, M represents the modulation depth,
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 space t The wave number of a representative surface wave,
representing the kronecker product of two matrices,
representative fetch matrix E rad The conjugate transpose of (a) is performed,
representative fetch matrix J surf P is a factor for controlling polarization, and radiates right-hand circularly polarized waves when p =1, radiates left-hand circularly polarized waves when p = -1, and radiates radiation-ray polarized waves when p = 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 out to be provided with slotted square metal patches and partial intermediate layer medium substrates, the size of the dug-out intermediate layer medium substrates 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 hole position. 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 micrometers;
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 1mm;
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 3.4mm. The numerical values are obtained through software optimization, the numerical values are applicable to the target frequency of 10GHz, and if the working frequency points need 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 eigenfrequency by using an eigenmode solver;
s2: randomly selecting one slotting angle of the square metal patch with the slot on the upper layer, simultaneously changing the side length, the total phase difference of a master boundary and a slave boundary and the transmission direction of the surface wave of the square metal patch with the slot on the upper layer, and solving equivalent scalar impedance through the intrinsic frequency obtained by calculation in S1;
s3: after the information of the equivalent scalar impedance calculated in the step S2 is analyzed, it is known that the size of the equivalent scalar impedance is related to the side length of the square metal patch with the slit on the upper layer 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 under the condition that the side length of the square metal patch with the slit on the upper layer is selected is firstly determined, and then each component of anisotropic tensor impedance is solved through a simultaneous equation set; then only changing the side length of the upper square metal patch with the slot at 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 S3 and the tensor impedance distribution relationship in 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: and (3) assuming that the refractive indexes of the square metal patch with the slot are consistent under two conditions of a plane and a micro-curve, establishing a conformal curve, bending the plane model of the holographic tensor impedance surface established in the S5 onto the conformal curve to form the conformal holographic tensor impedance surface, and then adding a feed monopole at the central position 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:
wherein, Z e Representing equivalent scalar impedance, Z 0 Which represents the impedance of the wave in free space,
and
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.
Furthermore, each component of the tensor impedance in step S3 needs to establish three sets of equivalent scalar impedance data of different surface wave transmission directions in parallel, and order
Can obtain Z xx 、Z yy And Z xy Wherein
Representing an equivalent scalar impedance, obtained by the following equation:
wherein eta is 0 Representing wave impedance in free space, θ t Represents 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 variable 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:
target wave:
from the holographic tensor impedance modulation formulation,
to obtain:
the specific expression of each component of the tensor impedance is obtained as follows:
wherein, J surf Representing a cylindrical surface wave generated by a feed monopole, E rad Representing an arbitrarily directed, arbitrarily polarized plane wave that needs to be generated, X representing the average impedance, M representing the modulation depth,
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, k0 representing the wave number of free space, and k representing the wave number of the free space t The wave number of the surface wave is represented,
representing the kronecker product of two matrices,
the representative taking matrix E rad The conjugate transpose of (a) is performed,
representative fetch matrix J surf Beta represents the phase factor of the outgoing beam after interference with the surface wave，E x And E Y The distribution represents the x-direction component and the y-direction component of E, J x And J Y The distribution represents the x-direction component and the y-direction component of J,
and
each represents E x And E Y The conjugate transpose of (a) is performed,
and
each represents J x And J Y P is a factor for controlling polarization, and is a wave that radiates right-hand circularly polarized waves when p =1, left-hand circularly polarized waves when p = -1, and radiation-ray polarized waves when p = 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 aperture efficiency of the conformal antenna based on the holographic tensor surface antenna designed by the scheme provided by the invention is improved by about 18 percent, and the conformal antenna can be combined with application scenes such as multi-beam generation and diffraction-free beam generation, and the like, so that the integration of the multifunction of the conformal curved antenna and the structural function of the antenna is 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 conformal surface wave antenna based on a holographic tensor impedance surface in accordance with 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 equivalent scalar impedance corresponding to tensor impedance of the present invention and a size of a square metal patch with a 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 a maximum value of equivalent scalar impedance corresponding to 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 (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;
FIG. 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 FIG. 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 a 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;
figure 13 (left) is a (30, 45) degree single beam simulated standing wave curve for a conformal holographic tensor impedance surface of the present invention, and figure 13 (right) is a (30, 45) degree single beam simulated axial ratio curve for a 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 conformal holographic tensor impedance surface of the invention, and figure 14 (right) is a (30, 45) degree single beam simulated three-dimensional gain pattern of the conformal holographic tensor impedance surface of the invention;
FIG. 15 is a tensor impedance distribution plot of a two-beam of the conformal holographic tensor impedance surface (30, 0), (30, 180) degrees 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 (30, 0), (30, 180) degrees dual beams of the present invention, and FIG. 17 (right) is a simulated axial ratio curve for the conformal holographic tensor impedance surface (30, 0), (30, 180) degrees dual beams of the present invention;
FIG. 18 (left) is a two-beam simulated two-dimensional gain pattern of the inventive conformal holographic tensor impedance surface (30, 0), (30, 180), and FIG. 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 is obvious 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 the term "disposed" in the present invention should be understood broadly, and for example, the connection may be fixed, or may be detachable, or may be connected through an intermediate medium, or may be connected 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 by 1mm, and the specific design flow 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 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 a refractive index error caused by size change, and solving an 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 the information of the equivalent scalar impedance calculated in the step S2 is analyzed, it is known that the size of the equivalent scalar impedance is related to the side length of the square metal patch with the slit on the upper layer 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 under the condition that the side length of the square metal patch with the slit on the upper layer is selected is firstly determined, 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 tensor impedance information corresponding to the side length and the transmission direction data of each group of square metal patches with the slots, and fitting tensor impedance pairsThe relationship between the maximum value of the corresponding equivalent scalar impedance and the side length of the square metal patch with the slot is as follows: z max ＝284.6*g 4 -1155*g 3 +1713*g 2 -1125*g 1 +453.1 wherein Z max Representing the maximum value of equivalent scalar impedance, g representing the difference of the side lengths of the upper layer square metal patch with the slit and the lower layer square metal floor, and drawing the relational expression 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:
radiation field:
from the holographic tensor impedance modulation formulation,
to obtain:
the expression for each component is then:
according to the above respective formulas, and bringing into the setting conditions of example 1
p = -1, ρ =219.4mm, array size 153.4mm, and then tensor impedance distribution calculated is shown in fig. 4.
S5: according to the above calculation and the fitting analysis in S3, the size of each impedance modulation unit on the wavefront and the slit angle are calculated, and a planar model of the entire holographic tensor impedance surface is established, as shown in fig. 5.
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, 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, and the simulated modeling graph is shown as figure 8The simulated standing wave curve is shown in fig. 9 (left), and the result shows that in the set frequency band, the reflection coefficients are all lower than-8 dB, the relative impedance bandwidth is more than 20%, the reflection coefficient at the 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 two-dimensional gain directional diagram and a three-dimensional gain directional diagram can achieve a gain of 17.7dBi, a side lobe level of-12.5 dB, and a reduced aperture efficiency of 17.9% (data for calculating the aperture efficiency is derived from the following calculation formula:
wherein G is 0 Denotes the absolute gain, A p The 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 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 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 CST, and the result shows that the radiation field has the characteristic of a high-gain single beam, which meets the design requirement, and the following details are described:
s1: establishing an impedance modulation unit model as shown in fig. 2, wherein the side length of the 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 the square metal floor on the lower layer is 3.4mm, the thickness of the 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 a refractive index error caused by size change, and solving an 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 the surface wave to be 0-170 degrees, and solving equivalent scalar impedance through the intrinsic frequency obtained through calculation;
s3: after the information of the equivalent scalar impedance calculated in the step S2 is analyzed, it is known that the size of the equivalent scalar impedance is related to the side length of the square metal patch with the slit on the upper layer 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 under the condition that the side length of the square metal patch with the slit on the upper layer is selected is firstly determined, 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: z max ＝284.6*g 4 -1155*g 3 +1713*g 2 -1125*g 1 +453.1 wherein Z max Representing the maximum value of equivalent scalar impedance, g representing the difference of the side lengths of the upper layer square metal patch with the slit and the lower layer square metal floor, and drawing the relational expression 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 a specific expression for each component of tensor impedance, a specific expression for the right-hand circularly polarized radiation field and the reference wave needs to be given:
reference wave:
radiation field:
from the holographic tensor impedance modulation formulation,
to obtain:
the expression for each component is then:
according to the above respective equations, and bringing into the setting conditions of example 2
p = +1, ρ =244mm, array size 153.4mm, and then tensor impedance distribution calculated is shown in fig. 11.
S5: according to the calculation and the fitting analysis in the step S3, the size and the slit angle of each impedance modulation unit on the wavefront are calculated, and a planar model of the entire holographic tensor impedance surface is established.
S6: and (4) establishing a conformal curved surface, bending the plane model of the holographic tensor impedance surface established in the S5 onto the curved surface to be conformal to form the conformal holographic tensor impedance surface, and then adding a feed monopole into the center of the conformal holographic tensor impedance surface to complete the whole design. Still, the surface wave can be excited better by using the curved feeding monopole with the tapered structure of the embodiment 1.
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 figure 12, the simulated standing wave curve is shown in figure 13 (left), and the result shows that all the reflection coefficients are lower than-10 dB, the relative impedance bandwidth is more than 20%, the reflection coefficient at the 10GHz working frequency band 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 side lobe level is-7.6 dB, the reduced aperture efficiency is 16%, the beam direction is (32, 50) degrees, slight deviation exists, 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 the 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 1mm, and the radiation waves are set to be circularly polarized symmetric dual beams with opposite rotation directions emitted by angles of (30, 0) and (30, 180), 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 a refractive index error caused by size change, and solving an 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 the equivalent scalar impedance information obtained by calculation in the S2 is analyzed, the fact that the size of the equivalent scalar impedance is related to the side length of the upper-layer square metal patch with the slot and the transmission direction of the surface wave is known, and the equivalent scalar impedance cannot be directly solved, therefore, the relation of the equivalent scalar impedance along with the transmission direction of the surface wave under the condition that the side length of the upper-layer square metal patch with the slot is selected is firstly determined, 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: z is a linear or branched member max ＝284.6*g 4 -1155*g 3 +1713*g 2 -1125*g 1 +453.1 wherein Z max Representing 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:
radiation field:
from the holographic tensor impedance modulation formulation,
we have found that:
the expression for each component is then:
according to the above respective formulas, and bringing into the setting conditions of example 3
ρ =244mm, array size 153.4mm by 153.4mm, and then the tensor impedance distribution calculated is shown in fig. 15.
S5: according to the calculation and the fitting analysis in the step S3, the size and the slit angle of each impedance modulation unit on the wavefront are calculated, and a planar model of the entire holographic tensor impedance surface is established.
S6: a conformal curved surface is established, the plane model of the holographic tensor impedance surface established in the step S5 is bent to 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. 16. Still, the surface wave can be excited better by using the curved feeding monopole with the tapered structure of the embodiment 1.
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 it will be apparent to those skilled in the art that various changes and modifications may be made without departing from the inventive concept of the present invention, and such changes and modifications are intended to fall within the scope of the present invention.
Claims (13)
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, wherein each impedance modulation unit comprises a square metal patch with a slot at the upper layer, a medium substrate at the middle layer and a square metal floor at the lower layer; the sizes of the square metal patches with slits on the upper layer of the m multiplied by n impedance modulation units are different, and the medium substrate of the middle layer and the square metal floor on the lower layer are all kept to be the same; the square metal patch with the slot is positioned on the medium substrateOn a central normal line, 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 angle of the slot is selected arbitrarily; 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: z max ＝284.6*g 4 -1155*g 3 +1713*g 2 -1125*g 1 +453.1 wherein Z max The maximum value of equivalent scalar impedance is represented, g represents the difference of the side length of the square metal patch with the slot and the square metal floor; selecting the curvature radius of the conformal curved surface to ensure that the characteristic of the impedance modulation unit after conformal 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:
target wave:
in the above formulae, J surf Representing a cylindrical surface wave generated by a feed monopole, E rad Representing plane waves of any direction and any polarization to be generatedThe above two waves are modulated as follows to form a tensor surface impedance distribution:
where X represents the average impedance, M represents the modulation depth,
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 space t The wave number of a representative surface wave,
representing the kronecker product of two matrices,
the representative taking matrix E rad The conjugate transpose of (a) is performed,
the representative fetch matrix J surf P is a factor for controlling polarization, and radiates right-hand circularly polarized waves when p =1, radiates left-hand circularly polarized waves when p = -1, and radiates radiation-ray polarized waves when p = 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 and are 35 microns thick.
5. The holographic tensor impedance surface based conformal surface wave antenna as recited in claim 1, wherein the dielectric substrate is a slab with a relatively high dielectric constant to achieve relatively large modulation depth and leakage efficiency.
6. The holographic tensor impedance surface-based conformal surface wave antenna of claim 5, wherein the dielectric substrate employs Rogers 3006 with a dielectric constant of 6.15 and a thickness of 1mm.
7. The holographic tensor impedance surface-based conformal surface wave antenna as recited in claim 1, wherein the slotted square metal patch has dimensions of 2.0mm to 3.3mm on a side, the slotted width of the slotted square metal patch is 0.15mm, and the square metal floor has a side of 3.4mm at a target frequency of 10 GHz.
8. 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.
9. The holographic tensor impedance surface based conformal surface wave antenna of any one of claims 1-8, wherein the feed monopole is a tapered feed monopole with a large top and a small bottom.
10. The method of designing a holographic tensor impedance surface based conformal surface wave antenna of any one of claims 1-9, 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 slot on the upper layer, simultaneously changing the side length, the total phase difference of a master boundary and a slave boundary and the transmission direction of the surface wave of the square metal patch with the slot on the upper layer, and solving equivalent scalar impedance through the intrinsic frequency obtained by calculation in S1;
s3: after the information of the equivalent scalar impedance calculated in the step S2 is analyzed, it is known that the size of the equivalent scalar impedance is related to the side length of the square metal patch with the slit on the upper layer 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 under the condition that the side length of the square metal patch with the slit on the upper layer is selected is firstly determined, 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 S3 and the tensor impedance distribution relationship in 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: and (3) assuming that the refractive indexes of the square metal patch with the slot are consistent under two conditions of a plane and a micro-curve, establishing a conformal curve, bending the plane model of the holographic tensor impedance surface established in the S5 onto the conformal curve to form the conformal holographic tensor impedance surface, and then adding a feed monopole at the central position of the conformal holographic tensor impedance surface to complete the whole design.
11. The design method according to claim 10, wherein the calculation of the equivalent scalar impedance in step S2 is performed according to the following equation:
wherein Z is e Represent an equivalent standardMagnitude impedance, Z 0 Which represents the impedance of the wave in free space,
and
the phase difference in the horizontal and vertical directions in 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.
12. The method of claim 10, 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
Can obtain Z xx 、Z yy And Z xy Wherein
Representing an equivalent scalar impedance, obtained by the following equation:
wherein eta is 0 Representing wave impedance in free space, θ t Represents the propagation direction of the surface wave, and j represents an imaginary unit.
13. The design method according to claim 10, 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:
target wave:
from the holographic tensor impedance modulation formulation,
to obtain:
the specific expression of each component of the tensor impedance is obtained as follows:
wherein, J surf Representing a cylindrical surface wave generated by a feed monopole, E rad Representing plane waves of arbitrary orientation and arbitrary polarization to be generated, and X represents average impedanceAnd M represents a modulation depth,
the pitch angle and the azimuth angle of an emergent beam are represented, x and y represent plane coordinates of the impedance modulation unit, r represents the radius of the impedance modulation unit on a plane, rho represents the curvature radius of the conformal curved surface, j represents an imaginary unit, k0 represents a free space wave number, and k represents the radius of the conformal curved surface t The wave number of the surface wave is represented,
representing the kronecker product of two matrices,
the representative taking matrix E rad The conjugate transpose of (a) is performed,
representative fetch matrix J surf Beta represents the phase factor after the interference of the outgoing beam and the surface wave, E x And E Y The distribution represents the x-direction component and the y-direction component of E, J x And J Y The distribution represents the x-direction component and the y-direction component of J,
and
each represents E x And E Y The conjugate transpose of (a) is performed,
and
each represents J x And J Y P is a factor controlling polarization, and radiates right-hand circularly polarized waves when p =1, radiates left-hand circularly polarized waves when p = -1, and radiates left-hand circularly polarized waves when p = -1 is usedWhen p =0, the wave is a radiation polarized wave.
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