CN113328239A - Periodic impedance modulation surface for arbitrary pitching surface rectangular beam forming - Google Patents

Periodic impedance modulation surface for arbitrary pitching surface rectangular beam forming Download PDF

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CN113328239A
CN113328239A CN202110504474.XA CN202110504474A CN113328239A CN 113328239 A CN113328239 A CN 113328239A CN 202110504474 A CN202110504474 A CN 202110504474A CN 113328239 A CN113328239 A CN 113328239A
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impedance
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李家林
汪宗林
赵青
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University of Electronic Science and Technology of China
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Abstract

The invention discloses a periodic impedance modulation surface for arbitrary pitching rectangular beam forming, and belongs to the technical field of antennas and periodic impedance modulation surfaces. Compared with the prior art of combining array synthesis and algorithm, the periodic impedance modulation surface provided by the invention does not need to adopt multiple feed sources and a complex feed network, only needs to prolong the inner core of the coaxial line to form a monopole for feeding, and has the advantages of simple structure and easiness in implementation. Another advantage of the present invention is that it can implement rectangular beamforming in a direction having a certain tilt angle compared to the existing method to implement rectangular beamforming in the normal direction.

Description

Periodic impedance modulation surface for arbitrary pitching surface rectangular beam forming
Technical Field
The invention belongs to the technical field of antennas and periodic impedance modulation surfaces, and particularly relates to a periodic impedance modulation surface for arbitrary pitching rectangular beam forming.
Background
An antenna plays an extremely important role in mobile communication as a terminal of a wireless communication system. The gain lobe of the electromagnetic wave transmitted by the traditional base station antenna is generally spherical, the lobe width is wide, and the gain drop is gentle on two sides of the main radiation direction, so that the electromagnetic wave signals transmitted between the antennas with different directions are interfered with each other, and then the requirement is provided for the rectangular wave beam forming technology with a certain roll-off rate so as to eliminate or reduce the mutual interference of the signals in a multi-beam multiplexing area.
The document "Flat-Top focused Pattern Synthesis Through the Design of the Arbitrary Planar-Shaped Apertures" realizes rectangular beam forming by two technologies, one is to obtain a directional diagram array with constant phase distribution by utilizing Rayleigh quotient; the other is based on a power synthesis technology, and no phase of an array directional diagram is required. The document "Synthesizing unified Amplitude array With Shaped Patterns by Joint Optimization of Element Positions, Rotations and Phases" realizes arbitrary Shaped beamforming by determining the position, rotation angle and phase excitation of each Element through a Joint Optimization algorithm.
However, in the prior art, beam forming is realized by adjusting and controlling the amplitude and the phase of the array by combining an optimization algorithm, but multiple feed sources are generally adopted, so that a complex feed network is required, the size/volume is large and difficult to realize, and the prior art only realizes normal rectangular beam forming and cannot realize rectangular beam forming on any pitch plane.
Disclosure of Invention
It is an object of the present invention to overcome the above-mentioned drawbacks of the prior art and to provide a periodic impedance modulation surface for arbitrary pitch rectangular beamforming.
The technical problem proposed by the invention is solved as follows:
a periodic impedance modulation surface for any pitching surface rectangular wave beam forming comprises a corner cut rectangular metal patch unit 1, a dielectric substrate 2, a metal grounding plate 3 and a monopole feed source 4; the corner-cut rectangular metal patch unit 1 is positioned on the upper surface of the dielectric substrate 2, and the metal ground plate 3 is positioned on the lower surface of the dielectric substrate 2; the overall shape of the periodic impedance modulation surface is circular, the periodic impedance modulation surface is divided into uniformly distributed crystal lattices, and the metal patch units 1 are limited in the crystal lattices;
the monopole feed source 4 adopts a coaxial line, the inner core of the coaxial line passes through the metal grounding plate 3 and the dielectric substrate 2 and extends into the space, and the outer conductor is connected with the metal grounding plate 3; the position of the upper surface of the dielectric substrate 2 corresponding to the monopole feed source 4 is not provided with the corner-cut rectangular metal patch unit 1;
the width a and the height b of the rectangular metal patch unit 1 at different positions are different from the counterclockwise rotation angle theta along the longitudinal axis, and the specific determination method is as follows:
step 1, modeling an impedance unit in electromagnetic simulation software, wherein the impedance unit comprises a corner cut rectangular metal patch unit 1, a lattice dielectric substrate and a metal grounding plate, setting periodic boundary conditions, performing parameter scanning by taking the width a and the height b of the corner cut unit metal patch 1 and a counterclockwise rotation angle theta along a longitudinal axis as variables to obtain a corresponding relation between patch size and tensor impedance distribution, and storing the corresponding relation as a database for later use;
step 2, giving an expected target field, and calculating the final impedance distribution of the periodic impedance surface;
step 2-1. given the desired target field EA：
Figure BDA0003057820020000021
Wherein E is0Representing the amplitude of the target field, kl (p) representing the phase factor of the target field, p being the radius value, eρ(p) and γρ(p) represents the amplitude and phase in the radial direction of the unit polarization vector,
Figure BDA0003057820020000022
the unit polar coordinates in the radial direction are expressed,
Figure BDA0003057820020000023
and
Figure BDA0003057820020000024
respectively representing the magnitude and phase of the azimuthal direction of the unit polarization vector,
Figure BDA0003057820020000025
indicating azimuthal directionPolar coordinates of the bits, j being an imaginary symbol;
step 2-2, giving the phase factor Ks (rho) of the surface impedance, the modulation coefficient m and the average impedance in the radius direction
Figure BDA0003057820020000026
And average impedance in the azimuthal direction
Figure BDA0003057820020000027
The current iteration number is made to be 1;
step 2-3. inverse solution of the propagation constant beta of the initial surface wavefield according to the following formulaSW：
Figure BDA0003057820020000028
Step 2-4, calculating the impedance distribution X of the periodic impedance surface of the current iteration times:
Figure BDA0003057820020000029
Figure BDA00030578200200000210
Figure BDA00030578200200000211
Figure BDA00030578200200000212
Figure BDA00030578200200000213
wherein, XρρAs the resistance component in the radial direction,
Figure BDA00030578200200000214
the coupling impedance components in the radial and azimuthal directions,
Figure BDA00030578200200000215
is the azimuthal direction impedance component; m isρ(rho) is the module value of the modulation coefficient in the radial direction, phiρ(p) is the radial direction modulation coefficient phase,
Figure BDA00030578200200000216
is the module value of the modulation coefficient in the azimuth direction,
Figure BDA0003057820020000031
modulating the coefficient phase for the azimuth direction;
step 2-5, making the updated
Figure BDA0003057820020000032
After updating
Figure BDA0003057820020000033
Inverse solution of the equation to update the propagation constant beta of the surface wavefieldSW：
Figure BDA0003057820020000034
Update the phase factor Ks (ρ) of the surface impedance:
Figure BDA0003057820020000035
wherein, betaΔ(ρ) is the difference in propagation constants of the surface wavefield after and before the update;
step 2-6, updating the modulation coefficient m:
Figure BDA0003057820020000036
Figure BDA0003057820020000037
Figure BDA0003057820020000038
Figure BDA0003057820020000039
Figure BDA00030578200200000310
Figure BDA00030578200200000311
Figure BDA00030578200200000312
the impedance distribution X of the periodic impedance surface is arranged in the form:
X＝X(0)+X(+1)+X(-1)
Figure BDA00030578200200000313
Figure BDA00030578200200000314
Figure BDA0003057820020000041
wherein j is0In order to be able to excite the amplitude of the field,
Figure BDA0003057820020000042
is a second class of first order Bessel function;
Figure BDA0003057820020000043
and
Figure BDA0003057820020000044
a ground dielectric impedance of zero order and negative first order, respectively;
step 2-6, judging whether a cut-off condition is met, if so, updating the phase factor Ks (rho) of the surface impedance, the modulation coefficient m and the average impedance in the radius direction
Figure BDA0003057820020000045
And average impedance in the azimuthal direction
Figure BDA0003057820020000046
Calculating the impedance distribution X of the final periodic impedance surface; otherwise, the current iteration times are made to be +1, and the step 2-3 is executed again;
the cutoff condition is that the current iteration number reaches the set maximum iteration number, or the difference between the updated modulation coefficient m and the modulation coefficient m before updating is smaller than a set threshold;
step 3, matching the impedance distribution of the final periodic impedance surface obtained by calculation in the step 2 with tensor impedance distribution in the database in the step 1, and finding out the patch size corresponding to the impedance distribution of the final periodic impedance surface according to the corresponding relation between the patch size and the tensor impedance distribution in the database;
step 4. give the desired target field E againA′：
Figure BDA0003057820020000047
Where kl (ρ) denotes the phase factor, γ'ρ(p) represents the phase in the radial direction of the unit polarization vector of the desired target field given again,
Figure BDA0003057820020000048
a phase representing the azimuthal direction of the unit polarization vector of the given desired target field again;
repeating the step 2 to the step 3 to obtain the patch size of the impedance distribution of the periodic impedance surface calculated corresponding to the preset expected target field; the patch sizes of the impedance distributions of the two resulting final periodic impedance surfaces are averaged.
Further, the overall shape of the periodic impedance modulation surface is circular, the radius corresponds to 5 times of the free space wavelength corresponding to the center frequency of 30GHz, the periodic impedance modulation surface is divided into uniformly distributed lattices, the side length of each lattice is 1/10 of the free space wavelength corresponding to the center frequency of 30GHz, and the metal patch unit 1 is confined in the lattice.
Further, the dielectric substrate 2 has a thickness h of 0.508mm and a relative dielectric constant of 10.2, and the shape and radius of the metal ground plate 3 are identical to those of the dielectric substrate 2.
The invention has the beneficial effects that:
compared with the prior art of combining array synthesis and algorithm, the periodic impedance modulation surface provided by the invention does not need to adopt multiple feed sources and a complex feed network, only needs to prolong the inner core of the coaxial line to form a monopole for feeding, and has the advantages of simple structure and easiness in implementation. Another advantage of the present invention is that it can implement rectangular beamforming in a direction having a certain tilt angle compared to the existing method to implement rectangular beamforming in the normal direction.
Drawings
FIG. 1 is a top view and a side view of the overall structure of a periodic impedance modulation surface according to the present invention;
FIG. 2 is a detailed view of a central portion of the periodic impedance modulation surface of the present invention;
FIG. 3 is a schematic diagram and a top view of a tensor impedance unit in an embodiment;
FIG. 4 is a rectangular coordinate gain pattern of the periodic impedance modulation surface in the XOZ plane of 30GHz in the embodiment;
FIG. 5 is a polar gain pattern of the periodic impedance modulation surface in the XOZ plane at 30GHz in the example;
FIG. 6 is a rectangular gain pattern of a section with a pitch angle of 37 degrees of a periodic impedance modulation surface in an embodiment;
fig. 7 is a three-dimensional gain pattern of a periodic impedance modulation surface in an embodiment.
Detailed Description
The invention is further described below with reference to the figures and examples.
The embodiment provides a periodic impedance modulation surface for arbitrary pitching rectangular beam forming, the top view and the side view of the whole structure of which are shown in fig. 1, and the detail view near the center part is shown in fig. 2, and the periodic impedance modulation surface comprises a corner cut rectangular metal patch unit 1, a dielectric substrate 2, a metal ground plate 3 and a monopole feed source 4; the corner-cut rectangular metal patch unit 1 is positioned on the upper surface of the dielectric substrate 2, and the metal ground plate 3 is positioned on the lower surface of the dielectric substrate 2;
the overall shape of the periodic impedance modulation surface is circular, the radius corresponds to 5 times of the free space wavelength corresponding to the center frequency of 30GHz, the periodic impedance modulation surface is divided into uniformly distributed lattices, the side length of each lattice is 1/10 of the free space wavelength corresponding to the center frequency of 30GHz, and the metal patch unit 1 is limited in the lattices. The thickness h of the dielectric substrate 2 is 0.508mm, the relative dielectric constant is 10.2, and the shape and radius of the metal grounding plate 3 are consistent with those of the dielectric substrate 2.
The monopole feed source 4 adopts a coaxial line, the inner core of the coaxial line passes through the metal grounding plate 3 and the dielectric substrate 2 and extends into the space, and the outer conductor is connected with the metal grounding plate 3. The position of the upper surface of the dielectric substrate 2 corresponding to the monopole feed source 4 is not provided with the corner-cut rectangular metal patch unit 1; in this embodiment, the 5 × 5 corner-cut rectangular metal patch unit 1 located at the center of the periodic impedance modulation surface is removed.
The width a and the height b of the rectangular metal patch unit 1 at different positions are different from the counterclockwise rotation angle theta along the longitudinal axis, and the specific determination method is as follows:
step 1, modeling an impedance unit in electromagnetic simulation software, wherein the structural schematic diagram of the impedance unit is shown in fig. 3, the impedance unit comprises a corner-cut rectangular metal patch unit 1, a lattice dielectric substrate and a metal grounding plate, a periodic boundary condition is set, parameter scanning is carried out by taking the width a and the height b of the corner-cut unit metal patch 1 and an anticlockwise rotation angle theta along a longitudinal axis as variables to obtain a corresponding relation between patch size and tensor impedance distribution, and the corresponding relation is stored as a database for later use;
step 2, giving an expected target field, and calculating the final impedance distribution of the periodic impedance surface;
step 2-1. given the desired target field EA：
Figure BDA0003057820020000061
Wherein E is0Representing the amplitude of the target field, kl (p) representing the phase factor of the target field, p being the radius value, eρ(p) and γρ(p) represents the amplitude and phase in the radial direction of the unit polarization vector,
Figure BDA0003057820020000062
the unit polar coordinates in the radial direction are expressed,
Figure BDA0003057820020000063
and
Figure BDA0003057820020000064
respectively representing the magnitude and phase of the azimuthal direction of the unit polarization vector,
Figure BDA0003057820020000065
representing the unit polar coordinate of the azimuth direction, and j is an imaginary number symbol;
step 2-2, giving the phase factor Ks (rho) of the surface impedance, the modulation coefficient m and the average impedance in the radius direction
Figure BDA0003057820020000066
And average impedance in the azimuthal direction
Figure BDA0003057820020000067
The current iteration number is made to be 1;
step 2-3. inverse solution of the propagation constant beta of the initial surface wavefield according to the following formulaSW：
Figure BDA0003057820020000068
Step 2-4, calculating the impedance distribution X of the periodic impedance surface of the current iteration times:
Figure BDA0003057820020000069
Figure BDA00030578200200000610
Figure BDA00030578200200000611
Figure BDA00030578200200000612
Figure BDA00030578200200000613
wherein, XρρAs the resistance component in the radial direction,
Figure BDA00030578200200000614
the coupling impedance components in the radial and azimuthal directions,
Figure BDA00030578200200000615
is the azimuthal direction impedance component; m isρ(rho) is the module value of the modulation coefficient in the radial direction, phiρ(p) is the radial direction modulation coefficient phase,
Figure BDA00030578200200000616
is the module value of the modulation coefficient in the azimuth direction,
Figure BDA00030578200200000617
modulating the coefficient phase for the azimuth direction;
step 2-5, making the updated
Figure BDA00030578200200000618
After updating
Figure BDA00030578200200000619
Inverse solution of the equation to update the propagation constant beta of the surface wavefieldSW：
Figure BDA00030578200200000620
Update the phase factor Ks (ρ) of the surface impedance:
Figure BDA0003057820020000071
wherein, betaV(ρ) is the difference in propagation constants of the surface wavefield after and before the update;
step 2-6, updating the modulation coefficient m:
Figure BDA0003057820020000072
Figure BDA0003057820020000073
Figure BDA0003057820020000074
Figure BDA0003057820020000075
Figure BDA0003057820020000076
Figure BDA0003057820020000077
Figure BDA0003057820020000078
the impedance distribution X of the periodic impedance surface is arranged in the form:
X＝X(0)+X(+1)+X(-1)
Figure BDA0003057820020000079
Figure BDA00030578200200000710
Figure BDA00030578200200000711
wherein j is0In order to be able to excite the amplitude of the field,
Figure BDA00030578200200000712
is a second class of first order Bessel function;
Figure BDA00030578200200000713
and
Figure BDA00030578200200000714
zero order and negative first order ground dielectric impedances, respectively.
Step 2-6, judging whether a cut-off condition is met, if so, updating the phase factor Ks (rho) of the surface impedance, the modulation coefficient m and the average impedance in the radius direction
Figure BDA00030578200200000715
And average impedance in the azimuthal direction
Figure BDA00030578200200000716
Calculating the impedance distribution X of the final periodic impedance surface; otherwise, the current iteration times are made to be +1, and the step 2-3 is executed.
The cutoff condition is that the current iteration number reaches the set maximum iteration number, or the difference between the updated modulation coefficient m and the modulation coefficient m before updating is smaller than the set threshold.
And 3, matching the final impedance distribution of the periodic impedance surface obtained by calculation in the step 2 with tensor impedance distribution in the database in the step 1, and finding out the patch size corresponding to the final impedance distribution of the periodic impedance surface according to the corresponding relation between the patch size and the tensor impedance distribution in the database.
Step 4. give the desired target field E againA′：
Figure BDA0003057820020000081
Where kl (ρ) denotes the phase factor, γ'ρ(p) represents the phase in the radial direction of the unit polarization vector of the desired target field given again,
Figure BDA0003057820020000082
a phase representing the azimuthal direction of the unit polarization vector of the given desired target field again;
repeating the step 2 to the step 3 to obtain the patch size of the impedance distribution of the periodic impedance surface calculated corresponding to the preset expected target field; the patch sizes of the impedance distributions of the two resulting final periodic impedance surfaces are averaged.
Fig. 4 and 6 are rectangular coordinate and polar coordinate directional diagrams with 0 degree azimuth angle and section gain varying with pitch angle, respectively, from which it can be known that the 3dB wave beam width is 25 degrees, i.e. pitch angle is 26 ° to 51 °, and maximum gain is 15.8 dB; fig. 5 is a rectangular coordinate pattern in which the gain of a section varies with the azimuth angle at a pitch angle of 37 degrees, and it can be seen that the sectional pattern is distributed like a pen, and the 3dB beam width is 13 degrees. Fig. 7 is a three-dimensional gain pattern of a periodic impedance modulation surface. As a result, the scheme realizes two-dimensional rectangular beamforming with a certain pitch angle.

Claims (3)

1. A periodic impedance modulation surface for arbitrary pitching surface rectangular wave beam forming is characterized by comprising a corner-cut rectangular metal patch unit (1), a dielectric substrate (2), a metal grounding plate (3) and a monopole feed source (4); the corner cutting rectangular metal patch unit (1) is positioned on the upper surface of the dielectric substrate (2), and the metal grounding plate (3) is positioned on the lower surface of the dielectric substrate (2); the overall shape of the periodic impedance modulation surface is circular, the periodic impedance modulation surface is divided into uniformly distributed crystal lattices, and the metal patch units (1) are limited in the crystal lattices;
the monopole feed source (4) adopts a coaxial line, the inner core of the coaxial line penetrates through the metal grounding plate (3) and the medium substrate (2) and extends into the space, and the outer conductor is connected with the metal grounding plate (3); the position of the upper surface of the dielectric substrate (2) corresponding to the monopole feed source (4) is not provided with a corner-cut rectangular metal patch unit (1);
the width a and the height b of the corner cutting rectangular metal patch unit (1) at different positions are different from the anticlockwise rotation angle theta along the longitudinal axis, and the specific determination method comprises the following steps:
step 1, modeling an impedance unit in electromagnetic simulation software, wherein the impedance unit comprises a corner cut rectangular metal patch unit (1), a lattice dielectric substrate and a metal grounding plate, setting periodic boundary conditions, performing parameter scanning by taking the width a and the height b of the corner cut unit metal patch (1) and the anticlockwise rotation angle theta along the longitudinal axis as variables to obtain the corresponding relation between the size of the patch and tensor impedance distribution, and storing the corresponding relation as a database for later use;
step 2, giving an expected target field, and calculating the final impedance distribution of the periodic impedance surface;
step 2-1. given the desired target field EA：
Figure FDA0003057820010000011
Wherein E is0Representing the amplitude of the target field, kl (p) representing the phase factor of the target field, p being the radius value, eρ(p) and γρ(p) represents the amplitude and phase in the radial direction of the unit polarization vector,
Figure FDA0003057820010000012
the unit polar coordinates in the radial direction are expressed,
Figure FDA0003057820010000013
and
Figure FDA0003057820010000014
respectively representing the magnitude and phase of the azimuthal direction of the unit polarization vector,
Figure FDA0003057820010000015
representing the unit polar coordinate of the azimuth direction, and j is an imaginary number symbol;
step 2-2, giving the phase factor Ks (rho) of the surface impedance, the modulation coefficient m and the average impedance in the radius direction
Figure FDA0003057820010000016
And average impedance in the azimuthal direction
Figure FDA0003057820010000017
The current iteration number is made to be 1;
step 2-3. inverse solution of the propagation constant beta of the initial surface wavefield according to the following formulaSW：
Figure FDA0003057820010000018
Step 2-4, calculating the impedance distribution X of the periodic impedance surface of the current iteration times:
Figure FDA0003057820010000019
Figure FDA0003057820010000021
Figure FDA0003057820010000022
Figure FDA0003057820010000023
Figure FDA0003057820010000024
wherein, XρρAs the resistance component in the radial direction,
Figure FDA0003057820010000025
the coupling impedance components in the radial and azimuthal directions,
Figure FDA0003057820010000026
is the azimuthal direction impedance component; m isρ(rho) is the module value of the modulation coefficient in the radial direction, fρ(p) is the radial direction modulation coefficient phase,
Figure FDA0003057820010000027
is the module value of the modulation coefficient in the azimuth direction,
Figure FDA0003057820010000028
modulating the coefficient phase for the azimuth direction;
step 2-5, making the updated
Figure FDA0003057820010000029
After updating
Figure FDA00030578200100000210
Inverse solution of the equation to update the propagation constant beta of the surface wavefieldSW：
Figure FDA00030578200100000211
Update the phase factor Ks (ρ) of the surface impedance:
Figure FDA00030578200100000212
wherein, betaV(ρ) is the difference in propagation constants of the surface wavefield after and before the update;
step 2-6, updating the modulation coefficient m:
Figure FDA00030578200100000213
Figure FDA00030578200100000214
Figure FDA00030578200100000215
Figure FDA00030578200100000216
Figure FDA00030578200100000217
Figure FDA00030578200100000218
Figure FDA0003057820010000031
the impedance distribution X of the periodic impedance surface is arranged in the form:
X＝X(0)+X(+1)+X(-1)
Figure FDA0003057820010000032
Figure FDA0003057820010000033
Figure FDA0003057820010000034
wherein j is0In order to be able to excite the amplitude of the field,
Figure FDA0003057820010000035
is a second class of first order Bessel function;
Figure FDA0003057820010000036
and
Figure FDA0003057820010000037
respectively zero order and negativeA first order ground dielectric impedance;
step 2-6, judging whether a cut-off condition is met, if so, updating the phase factor Ks (rho) of the surface impedance, the modulation coefficient m and the average impedance in the radius direction
Figure FDA0003057820010000038
And average impedance in the azimuthal direction
Figure FDA0003057820010000039
Calculating the impedance distribution X of the final periodic impedance surface; otherwise, the current iteration times are made to be +1, and the step 2-3 is executed again;
step 3, matching the impedance distribution of the final periodic impedance surface obtained by calculation in the step 2 with tensor impedance distribution in the database in the step 1, and finding out the patch size corresponding to the impedance distribution of the final periodic impedance surface according to the corresponding relation between the patch size and the tensor impedance distribution in the database;
step 4. give the desired target field E againA′：
Figure FDA00030578200100000310
Where kl (ρ) denotes the phase factor, γ'ρ(p) represents the phase in the radial direction of the unit polarization vector of the desired target field given again,
Figure FDA00030578200100000311
a phase representing the azimuthal direction of the unit polarization vector of the given desired target field again;
repeating the step 2 to the step 3 to obtain the patch size of the impedance distribution of the periodic impedance surface calculated corresponding to the preset expected target field; the patch sizes of the impedance distributions of the two resulting final periodic impedance surfaces are averaged.
2. The periodic impedance modulation surface for arbitrary pitch rectangular beamforming according to claim 1, wherein the overall shape of the periodic impedance modulation surface is circular with a radius corresponding to 5 times the free space wavelength corresponding to the center frequency of 30GHz, the periodic impedance modulation surface is divided into uniformly distributed lattices, each lattice has a side length of 1/10 times the free space wavelength corresponding to the center frequency of 30GHz, and the metal patch unit (1) is confined within the lattice.
3. A periodic impedance modulation surface for arbitrary pitch-plane rectangular beamforming according to claim 1, wherein the dielectric substrate (2) has a thickness h of 0.508mm, a relative dielectric constant of 10.2, and the shape and radius of the metal ground plate (3) are consistent with those of the dielectric substrate (2).
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Cited By (1)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
CN114552211A (en) * 2022-03-04 2022-05-27 电子科技大学 High-gain multi-beam periodic impedance modulation surface antenna loaded with EBG structure

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