CN112234352B - Spherical antenna housing with equal-product-ratio conformal mapping - Google Patents
Spherical antenna housing with equal-product-ratio conformal mapping Download PDFInfo
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- CN112234352B CN112234352B CN202010973861.3A CN202010973861A CN112234352B CN 112234352 B CN112234352 B CN 112234352B CN 202010973861 A CN202010973861 A CN 202010973861A CN 112234352 B CN112234352 B CN 112234352B
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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q1/00—Details of, or arrangements associated with, antennas
- H01Q1/42—Housings not intimately mechanically associated with radiating elements, e.g. radome
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Abstract
The invention relates to the technical field of antenna housing design, in particular to a spherical antenna housing with equal-area-ratio conformal mapping, wherein a plurality of periodic units are uniformly distributed on the spherical surface of the antenna housing; each period unit is not covered; the area of the spherical cap passing through the center point P of any periodic unit is in direct proportion to the area of the circle of the mapping point Q passing through the center point P; the area of the spherical crown is equal to the area of the spherical center of the radome and the area of the vertex P of the radome0The axis of (A) is a central axis; the area of the circle is defined by the radome vertex P0Perpendicular mapping point Q of0As the center of a circle; a mapping point Q of the central point P and a radome vertex P0Perpendicular mapping point Q of0Are positioned on the same horizontal plane; a plane with the mapping point Q as the origin and a tangent plane T with the center point P as the originPHas a local mapping relationship. The invention realizes the establishment of the conformal absorber on the spherical surface and meets the electrical characteristics of the antenna housing.
Description
Technical Field
The invention relates to the technical field of antenna housing design, in particular to a spherical antenna housing with equal-product-ratio conformal mapping.
Background
The spherical membrane is fixed on the airtight platform around the cut opening by a pressing plate, is tightened by a rope or is fixed by other methods, and is internally inflated. Its advantages are thin and uniform cover wall, good electric performance and wide band; the cover body is soft and convenient to fold, light in weight, small in size and convenient to transport, store and install.
The spherical radome surface uses an absorbing material, and a conformal absorber needs to be established on the spherical surface. Most conformal absorbing materials are studied cylindrically conformal, since it is only curved in one direction. When a conformal absorber is built on a spherical surface, there is no suitable equidistant mapping to place the planar elements onto a curved surface.
Therefore, it is difficult for the spherical radome with a conformal absorbing material to meet the electrical characteristics of the radome.
Disclosure of Invention
In order to solve the technical problem, the spherical radome with equal area ratio conformal mapping provided by the invention can realize the establishment of a conformal absorber on a spherical surface and meet the electrical characteristics of the radome.
According to the spherical radome with the equal-area-ratio conformal mapping, a plurality of periodic units are uniformly distributed on the spherical surface of the radome; each period unit is not covered;
the area of the spherical cap passing through the center point P of any period unit is in direct proportion to the area of the circle passing through the mapping point Q of the center point P; the area of the spherical crown is equal to the area of the spherical center of the radome and the area of the vertex P of the radome0The axis of (A) is a central axis; the circle area is defined by the radome vertex P0Perpendicular mapping point Q of0As the center of a circle;
a mapping point Q of the central point P and a radome vertex P0Perpendicular mapping point Q of0Are positioned on the same horizontal plane;
a plane with the origin at the mapping point Q and a tangent plane T with the origin at the center point PPHaving a local mapping relationship;
the periodic unit is in the shape of a double hexagonal ring;
the mapping point Q and the vertical mapping point Q0The horizontal plane is a vertical mapping surface of the antenna housing;
each period unit is linearly mapped with a corresponding mapping unit on a vertical mapping surface; the mapping unit and the corresponding period unit have a scaling relationship.
Further, the relationship between the spherical crown area and the circular area is as follows:
in the formula (1), ksIs a proportionality coefficient of rQIs Q to Q0Distance of (A), R0Is the distance P from the spherical center of the sphere, i.e. the spherical radius of the radome, thetaPIs the included angle between the radius of the spherical surface where the point P is located and the z axis.
Further, the periodic unit is a periodic unit of a circuit simulation wave-absorbing material.
Further, the outer ring of the periodic unit has a circumscribed circle with a radius d1；
The inner ring of the periodic unit has a circumscribed circle with a radius d2；d1＞d2；
The outer ring and the inner ring of the periodic unit are concentric, and the distance between the outer rings of the periodic units is g1(ii) a In each period unit, the distance between the inner ring and the outer ring is g2；g1＞0，g2＞0。
Further, the applicable conditions of the plane equivalence in the local mapping are as follows:
p/2R0＜sin(π/36) (2)
in formula (2), p is the period of the double hexagonal ring, R0Is the distance from P to the spherical center, i.e. the spherical radius of the radome.
Further, the mapping unit (2) linearly maps to the corresponding period unit (1) with a scaling factor of αsThe expression is:
in the formula (3), ksIs a proportionality coefficient, θPIs the angle between the radius of the sphere where the point P is located and the z-axis, rQIs Q to Q0The distance of (c).
Further, the scaling factor ks＝1。
Further, the scaling factor ks＝1.04。
In the present invention, each periodic unit is a conformal absorber; the spherical cap area is proportional to the circular area. By adopting the mode of equal product ratio, the design of the spherical radome is completed. The antenna cover provided by the invention not only meets the electrical characteristics of the antenna cover, but also can maximally keep the electromagnetic mutual coupling characteristics of the periodic unit distribution under the conformal condition. .
Drawings
In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings used in the description of the embodiments or the prior art will be briefly described below, it is obvious that the drawings in the following description are only some embodiments of the present invention, and for those skilled in the art, other drawings can be obtained according to the drawings without creative efforts.
FIG. 1 is a schematic structural diagram of an embodiment of the present invention, wherein (a) is a top view and (b) is a side view;
fig. 2 is a spherical conformal mapping diagram of a radome in an embodiment of the invention;
fig. 3 is a schematic structural diagram of a double hexagonal ring on the surface of the radome in the embodiment of the invention;
FIG. 4 is a graph illustrating the influence of different proportionality coefficients on the wave absorbing performance of the radome in the embodiment of the invention;
FIG. 5 is a diagram illustrating an analysis of the impact of different conformal mapping methods on wave-absorbing performance in an embodiment of the present invention;
fig. 6 is a comparative analysis diagram of simulation and actual measurement results of the wave absorption performance of the radome in the embodiment of the invention.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the drawings in the embodiments of the present invention, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
As shown in fig. 1 and 2, in the spherical radome with equal area ratio conformal mapping according to the present embodiment, a plurality of periodic units 1 are uniformly distributed on a spherical surface of the radome; each period unit 1 is not covered;
the area of the spherical cap passing through the center point P of any period unit 1 is in direct proportion to the area of the circle passing through the mapping point Q of the center point P; the area of the spherical crown is equal to the area of the spherical center of the radome and the area of the vertex P of the radome0The axis of (A) is a central axis; the area of the circle isAntenna housing vertex P0Perpendicular mapping point Q of0As the center of a circle;
a mapping point Q of the central point P and a radome vertex P0Perpendicular mapping point Q of0Are positioned on the same horizontal plane;
a plane with the mapping point Q as the origin and a tangent plane T with the center point P as the originPHas a local mapping relationship.
In this embodiment, the conformal material is periodically distributed on the spherical surface of the radome, and each periodic unit of the spherical surface is formed. If the spherical radome meets the electrical requirements, the relevant data of each period unit also needs to meet certain standards. And all the distributed periodic units on the antenna housing are obtained according to conformal mapping of the mapping units on the plane.
As shown in fig. 2, the mapping point Q and the vertical mapping point Q0The horizontal plane is a vertical mapping surface of the antenna housing;
each period unit 1 is linearly mapped with a corresponding mapping unit 2 on a vertical mapping plane.
The conformal mapping steps of the vertical mapping surface and the spherical surface of the antenna housing are as follows:
the vertical mapping surface is distributed with dot matrixes, each dot represents one mapping unit 2, and all the mapping units 2 are uncovered; the point in the lattice is the center of the corresponding mapping unit 2.
thereby, the radome vertex P is obtained0And a center point P of a certain periodic unit.
Step 4, taking the mapping unit where Q is located and the tangent plane T taking P as the originPEstablishing local mapping;
As shown in fig. 1 and 3, the periodic unit 1 is shaped like a double hexagonal ring, and similarly, each of the mapping units 2 is shaped like a double hexagonal ring. The material of the periodic unit 1 is a circuit simulation wave-absorbing material.
The applicable conditions of the plane equivalence in the local mapping are as follows:
p/2R0＜sin(π/36) (2)
in formula (2), p is the period of the double hexagonal ring, R0Is the distance from P to the spherical center, i.e. the spherical radius of the radome.
Since the spherical surface is an inextensible surface, the planar periodic units cannot be directly conformal on the spherical surface. To this end, the lattice distribution is separated from the cell structure, first of all the lattice of the vertical mapping surface is determined to a radius R0The mapping relation of the lattice on the spherical surface. Then, a plane with an arbitrary point Q in the dot matrix of the vertical mapping surface as an origin and a tangent plane T with a corresponding point P on the spherical dot matrix as an origin are setPAnd establishing a local mapping. Finally, through local mapping between two planes, mapping units (shown as grey hexagons in FIG. 2) at the Q point are linearly mapped to the P point by a certain scaling factor, so as to ensure that T is ensuredPThe conformal mapping of the units on the plane is conformal mapping, and the applicable condition of the plane equivalence in the local mapping is p/2R0＜sin(π/36)。
As shown in fig. 3, on the spherical surface, the material of the periodic unit 1 is a circuit simulation wave-absorbing material. The outer and inner rings of each periodic unit 1 are concentric. The distance between the outer rings of each periodic unit 1 is g1(ii) a The distance between the inner ring and the outer ring in each period unit 1 is g2；g1＞0，g2Is greater than 0. The outer ring of the periodic unit 1 has a circumscribed circle with a radius d1；d1＞d2。
As shown in FIG. 2, the points determined by the lattice distribution function under planar conditions are represented as Q (r) in polar coordinatesQ,φQ) Spherical coordinates of corresponding points on the spherical conformalityIs represented by P (R)0,θP,φP) Mapping two points to have the same azimuth angle phiQ＝φP. Setting a reference point Q0(0,0) with a corresponding point P mapped on the sphere0(R0,0,0). The total area of each periodic unit 1 on the plane is SQThe total area of each periodic unit on the spherical surface is SP。
Under equal-area-ratio conformal mapping conditions, the spherical conformality of the double hexagonal ring array is shown in fig. 1. In the plane with Q0The circumference passing through Q as the center of the circle is in direct proportion to the circumference passing through P by taking the z axis as the central axis, and the proportionality coefficient is ksThe mapping method is an expansion of hemispherical mapping based on stereoscopic projection, and although the lattice distribution on the plane is uniform, the lattice distribution generated by hemispherical mapping is gradually distant from top to bottom. In particular ksWhen 1, each unit of the periodic unit on the sphere is opposite to the reference point P0Mutual coupling distance of located unit and reference point Q of each unit pair in plane0The mutual coupling distance of the located units is the same, and the electromagnetic mutual coupling characteristic of the planar periodic unit distribution is kept to the maximum extent under the conformal condition.
The above-mentioned with Q0The relation between the area of the circle passing through Q as the center of the circle and the area of the spherical cap passing through P by taking the z axis as the central axis is as follows:
in the formula (1), ksIs a proportionality coefficient of rQIs Q to Q0Distance of (A), R0Is the distance P from the spherical center of the sphere, i.e. the spherical radius of the radome, thetaPIs the included angle between the radius of the spherical surface where the point P is located and the z axis.
The scaling factor is alphasThe expression of (a) is:
in the formula (3), ksIs a proportionality coefficient, θPIs the angle between the radius of the sphere where the point P is located and the z-axis, rQIs Q to Q0The distance of (c).
The following simulation is performed on the method described in this embodiment to illustrate the beneficial effects of the method described in this embodiment:
and simulating the spherical conformal double hexagonal ring structure type wave-absorbing metamaterial by adopting the spectral domain transformation method. As shown in FIG. 4, the structural parameter of the double hexagonal ring unit is p is 25.98m, epsilonr＝2.2，t1＝0.5mm，t2＝12.7mm，d1＝13.5mm，s1＝0.5mm，d2＝7mm，s2＝0.5mm，ROUT＝180Ω，RIN＝100Ω。
Figure 3 shows the geometric distribution of the planar double hexagonal ring units. Geometrically different sequence numbers indicate the number of cycles, which is in contrast to the case of both rings. The unit array can be easily printed on a plane or a cylinder. However, since the spherical surface is not developable, it cannot be projected directly on the spherical surface. And printing a double hexagonal ring unit pattern with the period of p on the dielectric substrate. Relative dielectric constant εrIs placed on a spherical metal surface separated by an air layer. Resistors are inserted on each side of the hexagonal ring. The resistance values of the outer ring and the inner ring are respectively ROUTAnd RIN。t1And t2Representing the air layer thickness.
The curvature radius of the spherical metal carrier of the radome is RM140mm, then has a radius of curvature R0＝RM+t2The size of the wave absorbing material is 152.7mm, the wave absorbing material is equivalent to the wavelength of 2GHz frequency, the change of curvature has obvious influence on the wave absorbing performance on the 2-8GHz frequency band, and the wave absorbing material belongs to the spherical conformal design under the condition of large curvature. The conformal wave-absorbing metamaterial for the spherical surface of the radome consists of 126 units, in order to reflect the influence of the spherical surface conformal to the wave-absorbing performance in a centralized manner and reduce the influence of the edge effect on the simulation result, a metal spherical carrier is cut, and an area without unit coverage is removed.
Simulation analysis of difference krUnder the conditions, the effect of spherical conformality on the absorption performance is shown in fig. 5. With ksI.e. between cellsThe mutual coupling action distance is increased in proportion, the wave absorbing frequency band of the conformal wave absorbing metamaterial with the spherical surface of the antenna cover is gradually narrowed, the wave absorbing performance in the effective wave absorbing frequency band is gradually improved, and the wave absorbing performance in the frequency band of 7.5-9GHz is gradually deteriorated. The invention furthest keeps the periodicity of the unit and the lattice distribution of the planar structure in the equal-product-ratio mapping mode, so that the influence of spherical conformality on the wave absorption performance is small, and except that the wave absorption performance at individual frequency points is poor, most frequency bands still keep certain broadband wave absorption characteristics. Selecting proper k through spherical conformality of a mapping mode of equal product ratiosThe broadband wave absorbing performance under the spherical conformal condition can be realized.
The equal product ratio mapping described in the present invention is compared with the remaining mapping methods. Setting a constant diameter mapping ratio proportionality coefficient krProportional coefficient k of equal-circumference ratio mappingcProportional coefficient k of sum-equal product ratio mappingsAre all 1. Under three conformal mapping modes, the wave absorbing performance of the spherical conformal wave absorbing metamaterial for the TE wave under a normal incidence condition is compared with the wave absorbing performance of the planar wave absorbing metamaterial, and the simulation result is shown in fig. 5. The wave-absorbing metamaterial with three mapping modes is subjected to wave-absorbing performance deterioration in different degrees due to spherical surface conformality, and wave-absorbing bandwidth is reduced. Equal path mapping krUnder the condition of 1, the wave absorption performance of the material in a 2-5GHz frequency band is poor; isoperimetric mapping kcUnder the condition of 1, the wave absorbing performance of the composite material in a 6-9GHz frequency band is obviously deteriorated; equal product mapping ksUnder the condition of 1, compared with a plane wave-absorbing metamaterial, the wave-absorbing frequency band is slightly narrowed, and the wave-absorbing performance in the frequency band of 3-5GHz is slightly poor. Compared with the former two conformal mapping modes, the spherical conformal of the planar structure type wave-absorbing metamaterial under the condition of equal volume ratio has the minimum influence on the wave-absorbing performance.
Over-optimized selection ks1.04, mapping the spherical conformal double hexagonal ring structure type wave-absorbing metamaterial. The actually processed spherical conformal sample is a spherical crown structure with the radius of 140mm, the height of the spherical crown is 95.1mm, a hexagon with the side length of 151.6mm is used as a boundary to cut the spherical conformal sample, an area without a unit covering metal boundary is removed, and the influence of the metal edge is reduced.
Spherical capThe position of the mounting hole is determined by an equal-product-ratio mapping mode, and the position precision of the hole position is ensured by adopting a 3D printing mold. Printing double hexagonal ring units on dielectric constant epsilonrFR4 dielectric substrate of 2.2, with a loss tangent tan σ of 0.001, and mounted conformally one by one on a spherical carrier. On the wave-absorbing metamaterial with uniform resistance loading, the resistors on all the units are the same as ROUT180 Ω and RIN＝100Ω。
The results of comparative analysis of the RCS reduction effect of horizontally and vertically polarized waves at normal incidence are shown in fig. 6. Electric field direction E of horizontal and vertical polarized incidencexAnd EyAnd the oblique incident angle θ in the horizontal direction are respectively defined in the simulation experiment. By optimizing the parameter ksGood broadband absorption characteristics are realized 1.04, RCS reduction is better than 8dB in a frequency band of 2.7-8.5GHz, and simulation and actual measurement results are well matched. Because the units have central symmetry, the spherical conformal wave-absorbing metamaterial has similar wave-absorbing characteristics to two polarized waves.
In summary, the method of the present embodiment can realize the design of the spherical radome, and maintain the electromagnetic mutual coupling characteristics of the periodic unit distribution to the maximum extent under the conformal condition. Selecting proper k through spherical conformality of a mapping mode of equal product ratiosThe broadband wave absorbing performance under the spherical conformal condition can be realized.
It should be understood that the specific order or hierarchy of steps in the processes disclosed is an example of exemplary approaches. Based upon design preferences, it is understood that the specific order or hierarchy of steps in the processes may be rearranged without departing from the scope of the present disclosure. The accompanying method claims present elements of the various steps in a sample order, and are not intended to be limited to the specific order or hierarchy presented.
In the foregoing detailed description, various features are grouped together in a single embodiment for the purpose of streamlining the disclosure. This method of disclosure is not to be interpreted as reflecting an intention that the claimed embodiments of the subject matter require more features than are expressly recited in each claim. Rather, as the following claims reflect, invention lies in less than all features of a single disclosed embodiment. Thus, the following claims are hereby expressly incorporated into the detailed description, with each claim standing on its own as a separate preferred embodiment of the invention.
The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present invention. To those skilled in the art; various modifications to these embodiments will be readily apparent, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.
What has been described above includes examples of one or more embodiments. It is, of course, not possible to describe every conceivable combination of components or methodologies for purposes of describing the aforementioned embodiments, but one of ordinary skill in the art may recognize that many further combinations and permutations of various embodiments are possible. Accordingly, the embodiments described herein are intended to embrace all such alterations, modifications and variations that fall within the scope of the appended claims. Furthermore, to the extent that the term "includes" is used in either the detailed description or the claims, such term is intended to be inclusive in a manner similar to the term "comprising" as "comprising" is interpreted when employed as a transitional word in a claim. Furthermore, any use of the term "or" in the specification of the claims is intended to mean a "non-exclusive or".
The above-mentioned embodiments are intended to illustrate the objects, technical solutions and advantages of the present invention in further detail, and it should be understood that the above-mentioned embodiments are merely exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (8)
1. A spherical radome with equal area ratio conformal mapping is characterized in that a plurality of periodic units (1) are uniformly distributed on the spherical surface of the radome; each period unit (1) is not covered;
the area of the spherical crown passing through the center point P of any periodic unit (1) is in direct proportion to the area of the circle of the mapping point Q passing through the center point P; the area of the spherical crown is equal to the area of the spherical center of the radome and the area of the vertex P of the radome0The axis of (A) is a central axis; the circle area is defined by the radome vertex P0Perpendicular mapping point Q of0As the center of a circle;
a mapping point Q of the central point P and a radome vertex P0Perpendicular mapping point Q of0Are positioned on the same horizontal plane;
a plane with the origin at the mapping point Q and a tangent plane T with the origin at the center point PPHaving a local mapping relationship;
the periodic unit is in the shape of a double hexagonal ring;
the mapping point Q and the vertical mapping point Q0The horizontal plane is a vertical mapping surface of the antenna housing;
each period unit (1) is linearly mapped with a corresponding mapping unit (2) on a vertical mapping surface; the mapping unit (2) and the corresponding period unit (1) have a scaling relationship.
2. The spherical radome of claim 1, wherein the spherical cap area and the circular area have a relationship of:
in the formula (1), ksIs a proportionality coefficient of rQIs Q to Q0Distance of (A), R0Is the distance P from the spherical center of the sphere, i.e. the spherical radius of the radome, thetaPIs the included angle between the radius of the spherical surface where the point P is located and the z axis.
3. The spherical radome of claim 1, wherein the periodic elements are periodic elements of a circuit analog wave absorbing material.
4. The spherical radome of claim 1 wherein the outer ring of periodic elements has a circumscribing circle with a radius d1；
The inner ring of the periodic unit has a circumscribed circle with a radius d2；d1＞d2；
The outer ring and the inner ring of the periodic unit are concentric, and the distance between the outer rings of the periodic units is g1(ii) a In each period unit, the distance between the inner ring and the outer ring is g2；g1＞0，g2＞0。
5. The spherical radome of claim 1, wherein the applicable conditions for the equivalent of the mid-plane of the local mapping are as follows:
p/2R0<sin(π/36) (2)
in formula (2), p is the period of the double hexagonal ring, R0The distance from P to the spherical center of the sphere, namely the spherical radius of the radome.
6. The spherical radome of claim 1 wherein the scaling factor of the mapping units (2) to linearly map to corresponding periodic units (1) is αsThe expression is:
in the formula (3), ksIs a proportionality coefficient, θPIs the angle between the radius of the sphere where the point P is located and the z-axis, rQIs Q to Q0The distance of (c).
7. The spherical radome of claim 2 wherein the scaling factor k is equal to the conformal mappings＝1。
8. The spherical radome of claim 2 wherein the scaling factor k is equal to the conformal mappings＝1.04。
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