CN112164139B - Spherical surface equal-circumferential-ratio conformal mapping method for antenna housing - Google Patents
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Abstract
The invention relates to the technical field of antenna housing design, in particular to a method for designing a radomeA spherical surface isoperimetric ratio conformal mapping method related to an antenna housing 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 alphacLinear mapping to the sphere of P is performed such that Q is given0The circumference passing through Q as the center of the circle is proportional to the circumference passing through P with the z-axis as the central axis. The invention can design and realize the antenna housing with the spherical surface and ensure small mapping deformation.
Description
Technical Field
The invention relates to the technical field of antenna housing design, in particular to a spherical surface equal circumferential ratio conformal mapping method of 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 surface iso-circumferential ratio conformal mapping method for the radome provided by the invention can design and realize the radome with the spherical surface.
The spherical surface equi-circumferential-ratio conformal mapping method for the antenna housing provided by the invention 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 sphere along z-axisCorresponding point P on0Mapping 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 alphacLinear mapping to the sphere of P is performed such that Q is given0The circumference passing through Q as the center of the circle is proportional to the circumference passing through P with the z-axis as the central axis.
Further, the Q is0The relation between the circumference passing through Q as the center of circle and the circumference passing through P with the Z axis as the central axis is as follows:
kc2πrQ＝2πR0sinθP (1)
in the formula (1), kcIs 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 is αcThe expression of (a) is:
αc＝min(kc,1) (3)
in the formula (3), kcIs a scaling factor.
Preferably, the scaling factor kc≥1。
In the invention, each periodic unit on the plane can be mapped on the surface spherical surface of the antenna housing, and the deformation of the periodic unit can be ensured to be minimum when the spherical surface is conformal.
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 an analysis diagram of the influence of different proportionality coefficients on the wave absorbing 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, the spherical iso-circumferential 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. building (2)Erecting the surface sphere of the radome, 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 of the planar periodic cells is determined to a radius 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 by a scaling factor through the 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 alphacLinear mapping to the sphere of P is performed such that Q is given0The circumference passing through Q as the center of the circle is proportional to the circumference passing through P with the z-axis as the central axis.
The above-mentioned with Q0The relation between the circumference passing through Q as the center of circle and the circumference passing through P with the Z axis as the central axis is as follows:
kc2πrQ＝2πR0sinθP (1)
in the formula (1), kcIs 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 the equal-perimeter-ratio conformal mapping conditions, the spherical conformality of the double hexagonal ring array is shown in fig. 3. 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 kcThe 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. The distribution interval of the units on the spherical surface is larger, and when k iscWhen the cell size is larger than or equal to 1, the cell does not need to be reduced to avoid overlapping, the scaling coefficient of the cell is irrelevant to the position, so that the shapes of all the cells are the same, and the scaling coefficient alpha of the cell is introducedc。
The scaling factor is alphacThe expression of (a) is:
αc＝min(kc,1) (3)
in the formula (3), kcIs a scaling factor.
In the present embodiment, the proportionality coefficient kc≥1。
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 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. A double hexagonal ring unit pattern of period p is printed 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。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 difference kcUnder the conditions, the effect of spherical conformality on the absorption performance is shown in fig. 5. Under the condition of the mapping, the mapping is carried out,can ensure the minimum deformation of the unit when the spherical surface is conformal, when k iscWhen the wave absorbing capacity is more than or equal to 1, the structural sizes of all units are the same, and the wave absorbing capacity ratio kcIs better than 1.
In summary, the method according to the embodiment can realize the design of the spherical radome, each period unit on the plane can be mapped on the surface spherical surface of the radome, and each mapped period unit can be deformed little.
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 (6)
1. A spherical surface equi-circumferential 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 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 alphacLinear mapping to the sphere of P is performed such that Q is given0The circumference passing through Q as the center of the circle is proportional to the circumference passing through P with the z-axis as the central axis.
2. The spherical equi-circumferential-ratio conformal mapping method for the radome of claim 1, wherein the Q is0The relation between the circumference passing through Q as the center of circle and the circumference passing through P with the z-axis as the central axis is as follows:
kc2πrQ＝2πR0sinθP (1)
in the formula (1), kcIs 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 equal circumferential ratio conformal mapping method for the radome of claim 1, wherein the shape of the periodic unit is a double hexagonal ring.
4. The spherical equi-circumferential-ratio conformal mapping method for the radome of claim 3, wherein the applicable conditions of the local mapping mid-plane equivalence are as follows:
p/2R0<sin(π/36) (2)
in the 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 spherical equi-circumferential-ratio conformal mapping method for the radome of claim 1, wherein the scaling factor is αcThe expression of (a) is:
αc＝min(kc,1) (3)
in the formula (3), kcIs a scaling factor.
6. The spherical equi-circumferential-ratio conformal mapping method for the radome of claim 2, wherein the proportionality coefficient k isc≥1。
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| CN104752821A (en) * | 2015-03-06 | 2015-07-01 | 周丰峻 | Method for quickly establishing spherical antenna cover with metal latticed shell structure |
| CN104835117A (en) * | 2015-05-11 | 2015-08-12 | 合肥工业大学 | Spherical panorama generating method based on overlapping way |
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| US9130611B2 (en) * | 2012-08-17 | 2015-09-08 | Qualcomm Incorporated | Method of using zoning map for beam searching, tracking and refinement |
| US20190334255A1 (en) * | 2018-04-25 | 2019-10-31 | Bae Systems Information And Electronic Systems Integration Inc. | Modular/scalable antenna array design |
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| CN104752821A (en) * | 2015-03-06 | 2015-07-01 | 周丰峻 | Method for quickly establishing spherical antenna cover with metal latticed shell structure |
| CN104835117A (en) * | 2015-05-11 | 2015-08-12 | 合肥工业大学 | Spherical panorama generating method based on overlapping way |
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