CN112186351B - Spherical equal-area-ratio conformal mapping method for antenna housing - Google Patents
Spherical equal-area-ratio conformal mapping method for antenna housing Download PDFInfo
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- CN112186351B CN112186351B CN202010973867.0A CN202010973867A CN112186351B CN 112186351 B CN112186351 B CN 112186351B CN 202010973867 A CN202010973867 A CN 202010973867A CN 112186351 B CN112186351 B CN 112186351B
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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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- H—ELECTRICITY
- H01—ELECTRIC ELEMENTS
- H01Q—ANTENNAS, i.e. RADIO AERIALS
- H01Q17/00—Devices for absorbing waves radiated from an antenna; Combinations of such devices with active antenna elements or systems
- H01Q17/008—Devices for absorbing waves radiated from an antenna; Combinations of such devices with active antenna elements or systems with a particular shape
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Abstract
The invention relates to the technical field of antenna housing design, in particular to a spherical equal-area-ratio conformal mapping method of an antenna housing, which comprises the following steps: establishing a mapping plane located on an x axis and a y axis; the plane is distributed with dot matrixes, each point represents a period unit, and all the period units are not covered; determining a point Q in a lattice0Finding any point Q in the dot matrix as a circle center; establishing a surface sphere of the radome, and mixing Q0Mapping to a corresponding point P on a sphere along the z-axis0Mapping Q to a corresponding point P on the spherical surface; establishing local mapping between the unit of Q and the tangent plane with P as the origin; the unit of Q is scaled by a scaling factor of alphasLinear mapping to the sphere of P is performed such that Q is given0The area of the circle passing through Q as the center of the circle is in direct proportion to the area of the spherical crown passing through P by taking the z axis as the central axis. According to the invention, each periodic unit on the plane can be mapped on the surface spherical surface of the radome, and the electromagnetic mutual coupling characteristic of the periodic unit distribution is maintained to the maximum extent under the conformal condition.
Description
Technical Field
The invention relates to the technical field of antenna housing design, in particular to a spherical equal-area-ratio conformal mapping method for an antenna housing.
Background
The use of absorbing materials on the radome surface, most conformal absorbing materials are studied cylindrically conformal, since it is only curved in one direction. However, when building a conformal absorber on a two-dimensional spherical surface, for example on a sphere, there is no suitable equidistant mapping to place the planar elements on the curved surface. This makes the design and implementation of radome conformal absorbers more difficult.
Disclosure of Invention
In order to solve the technical problem, the spherical equal-area-ratio conformal mapping method for the radome provided by the invention can design and realize the radome with the spherical surface.
The invention provides a spherical equal-area-ratio conformal mapping method for an antenna housing, which comprises the following steps:
establishing a mapping plane located on an x axis and a y axis; the plane is distributed with dot matrixes, each point represents a period unit, and all the period units are not covered;
determining a point Q in a lattice0Taking the center of a circle, and finding any point Q in the dot matrix;
establishing a surface sphere of the radome, and mixing Q0Mapping to a corresponding point P on a sphere along the z-axis0Mapping Q to a corresponding point P on the spherical surface;
establishing local mapping between the unit of Q and the tangent plane with P as the origin;
the unit of Q is scaled by a scaling factor of alphasLinear mapping to the sphere of P is performed such that Q is given0The area of the circle passing through Q as the center of the circle is in direct proportion to the area of the spherical crown passing through P by taking the z axis as the central axis.
Further, the Q is0The 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.
Further, the shape of the periodic unit is a double hexagonal ring.
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.
In the above technical solution, the scaling factor isαsThe 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).
Preferably, the scaling factor ks＝1。
Preferably, the scaling factor ks＝1.04。
In the invention, each periodic unit on the plane can be mapped on the surface spherical surface of the radome, and the electromagnetic mutual coupling characteristic of the periodic unit distribution is maintained 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.
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 flow chart of a method according to an embodiment of the present invention;
fig. 2 is a spherical conformal mapping diagram of a radome in an embodiment of the invention;
fig. 3 is a spherical conformal view of a radome in an embodiment of the invention, wherein (a) is a top view and (b) is a side view;
fig. 4 is a schematic structural diagram of a double hexagonal ring on the surface of the radome in the embodiment of the invention;
FIG. 5 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. 6 is a diagram illustrating an analysis of the impact of different conformal mapping modes on wave absorption performance in an embodiment of the present invention;
fig. 7 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 obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention.
As shown in fig. 1, the spherical equal-area-ratio conformal mapping method for the radome provided in this embodiment includes:
101. establishing a mapping plane located on an x axis and a y axis; the plane is distributed with dot matrixes, each point represents a period unit, and all the period units are not covered;
in this embodiment, the periodic units are in the shape of double hexagonal rings, and the intervals between the periodic units are the same.
102. Determining a point Q in a lattice0Taking the center of a circle, and finding any point Q in the dot matrix;
103. establishing a surface sphere of the radome, and mixing Q0Mapping to a corresponding point P on a sphere along the z-axis0Mapping Q to a corresponding point P on the spherical surface;
104. tangent plane T with Q unit and P as originPEstablishing local mapping;
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-to-radius of the planar periodic cells is determinedIs R0The mapping relationship of the lattice on the sphere is shown in fig. 2. Then, a plane with an arbitrary point Q as an origin in the plane lattice and a tangent plane T with a corresponding point P as an origin in the spherical lattice are setPAnd establishing a local mapping. Finally, the cells at the point Q (shown as gray hexagons in FIG. 2) are linearly mapped to the point P with a scaling factor by local mapping between the two planes to ensure TPThe 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)。
On the spherical surface, the material of the periodic unit is a circuit simulation wave-absorbing material. The outer and inner rings of each periodic unit are concentric. The distance between the outer rings of each periodic unit is g1(ii) a In each period unit, the distance between the inner ring and the outer ring is g2；g1＞0，g2＞0。
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) The corresponding point on the spherical conformal surface is P (R) in the spherical coordinate system0,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 on the plane is SQThe total area of each periodic unit on the spherical surface is SP。
105. The unit of Q is scaled by a scaling factor of alphasLinear mapping to the sphere of P is performed such that Q is given0The area of the circle passing through Q as the center of the circle is in direct proportion to the area of the spherical crown passing through P by taking the z axis as the central axis.
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.
Under equal-area-ratio conformal mapping conditions, the spherical conformality of the double hexagonal ring array is shown in fig. 3. In the plane with Q0The area of a circle passing through Q as the center of the circle is in direct proportion to the area of a spherical crown passing through P by taking the z axis as a 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 equal to 1, each unit of the periodic unit on the sphere is opposite to the reference point P0Mutual coupling distance of located units 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 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).
In the present embodiment, the proportionality coefficient ks＝1。
Or, the proportionality coefficient ks＝1.04。
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 4 shows the geometric distribution of 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. A double hexagonal ring unit pattern of period p is printed on a 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。t1Represents the thickness of the dielectric layer, t2Representing the air layer thickness. The external circle of the external ring of the double hexagonal ring has the radius d1And the radius of the circumscribed circle of the inner ring is d2. Because the outer ring and the inner ring in the double-hexagon ring are both in a regular hexagon structure, the radius of the corresponding external circle is equal to the side length of the ring.
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 curvature change 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 different ksUnder the conditions, the effect of spherical conformality on the absorption performance is shown in fig. 5. With ksThe mutual coupling distance between the units 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 7.5-9GHz frequency band is gradually deteriorated. The invention furthest keeps the periodicity of the distribution of units and lattices of a planar structure in the equal-product-ratio mapping mode, so that the spherical conformal wave-absorbing performance is ensuredThe influence of (2) is small, and except that the wave absorbing performance at individual frequency points is poor, most frequency bands still keep certain broadband wave absorbing 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-to-equal 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. 6. The wave-absorbing metamaterial with the spherical conformal surface and three mapping modes causes the wave-absorbing performance to be poor in different degrees, and the 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, the wave-absorbing frequency band is slightly narrower than that of a plane wave-absorbing metamaterial, 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 ksThe spherical conformal double hexagonal ring structure type wave-absorbing metamaterial is mapped by an equal-area ratio of 1.04. 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.
The position of the mounting hole on the spherical crown is determined by an equal-volume-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 each unit are the sameROUT180 Ω and RIN＝100Ω。
The RCS reduction effect of the horizontal and vertical polarized waves at normal incidence was comparatively analyzed, and the simulation and actual measurement results are shown in fig. 7. 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 ksThe good broadband absorption characteristic is realized by 1.04, the RCS reduction of the broadband absorption characteristic is better than 8dB in the frequency band of 2.7-8.5GHz, and the simulation result is better matched with the actual measurement result. 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 (7)
1. A spherical equal-area-ratio conformal mapping method for an antenna housing is characterized by comprising the following steps:
establishing a mapping plane located on an x axis and a y axis; the plane is distributed with dot matrixes, each point represents a period unit, and all the period units are not covered;
determining a point Q in a lattice0Is used as the center of a circle,finding any point Q in the lattice;
establishing a surface sphere of the radome, and mixing Q0Mapping to a corresponding point P on a sphere along the z-axis0Mapping Q to a corresponding point P on the spherical surface;
establishing local mapping between the unit of Q and the tangent plane with P as the origin;
the unit of Q is scaled by a scaling factor of alphasLinear mapping to the sphere of P is performed so that Q is0The area of the circle passing through Q as the center of the circle is in direct proportion to the area of the spherical crown passing through P by taking the z axis as the central axis.
2. The method for spherical equal-area-ratio conformal mapping of a radome of claim 1, wherein the Q is0The 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.
3. The method for spherical equal-area-ratio conformal mapping of a radome of claim 1, wherein the periodic units are shaped as double hexagonal rings.
4. The method for conformal mapping of spherical equal-area-ratio of the radome of claim 3, wherein the applicable condition of the plane equivalence in the local mapping is 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.
5. The method for conformal mapping of spherical equal-area-ratio of a radome of claim 1, wherein the scaling factor is αsThe 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).
6. The method for spherical equal-area-ratio conformal mapping of a radome of claim 2, wherein the proportionality coefficient k iss＝1。
7. The method for spherical equal-area-ratio conformal mapping of a radome of claim 2, wherein the proportionality coefficient k iss＝1.04。
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