JPH0365042B2 - - Google Patents

Description

[Detailed description of the invention]

The present invention relates to a high-performance double-reflector antenna that can scan an antenna beam over a wide angle range and can also be used as a multi-beam antenna. A conventional double-reflector antenna will be explained using a torus antenna as an example. FIG. 1 shows a conventional torus antenna that can scan the antenna beam while keeping the main reflecting mirror fixed. In the figure, 1 indicates the main reflecting mirror surface, 3 indicates the position of the feeding horn (primary radiator), and 7 indicates the antenna aperture surface. The cross-sectional curve 4 in the y-z plane is the point 2 in the y-z plane.
It is a parabola having a focal point at 0, and the main reflecting mirror surface is given as a mirror surface obtained by rotating the parabola around the y-axis or the y'-axis 5, which forms a certain angle with the y-axis in the y-z plane, as the rotation axis. Therefore, by rotating the feeding horn 3 around the rotation axis 5 while keeping the main reflecting mirror 1 fixed, the antenna beam can be scanned over a wide angle. The torus antenna having this configuration has the drawback that the optical path length from the feeding horn 3 to the aperture surface 7 via the main reflecting mirror 1 is not constant, resulting in aberrations (phase errors) and a decrease in gain. In order to eliminate this drawback, a torus antenna with a sub-reflector 2 as shown in FIG. 2 is also being considered so that the optical path length is constant.
[Kreutel (R, Kreutel): For sanitary communication 20/
30GHz band multi-beam torus reflector antenna
for20／30GHz satellite communications
systems), AIAA 6th Communications
Satellite Systems Conference No. 76-302] However, the conventional torus antenna as described above has the disadvantage that the mapping of the electric field distribution of the feeding horn projected onto the antenna aperture is generally distorted into a "rice ball shape". FIG. 3a shows an example of a mapping of the conventional torus antenna shown in FIG. In this case, the electric field strength of the primary radiator 3 is assumed to have a distribution in which equal level lines are concentric circles as shown in FIG. 3b. As described above, conventional torus antennas have the disadvantage that the mapping of the electric field distribution of the feeding horn of the antenna is distorted, resulting in deterioration of cross-polarization characteristics and tracking characteristics using higher-order modes. In addition, large-diameter aperture antennas are used in earth stations for satellite communications, and this type of antenna is generally configured to drive the entire large-diameter reflector system in order to track the satellite. The disadvantage was that a large-scale drive system was required. Additionally, during strong winds such as typhoons, the antenna was fixed to protect the mirror surface, resulting in a loss of communication. The present invention has been made in view of the above points, and its purpose is to have no aberration at all on the aperture surface, extremely little distortion of the mapping of the electric field distribution of the feeding horn projected onto the aperture surface, and to provide a main reflecting mirror. An object of the present invention is to provide a multi-reflector antenna capable of beam scanning over a wide angle range while being fixed. Whereas the main reflector cross-sectional curve of a conventional torus antenna is given by a parabola, the present invention calculates a cross-sectional curve that maps to the aperture plane as desired, and converts this cross-sectional curve into a shape that is within the aperture plane. A new mirror system consisting of a main reflecting mirror that is rotated around a rotational axis or a rotational axis that has a predetermined angle with the aperture surface, and a sub-reflecting mirror that is formed based on this main reflecting mirror to eliminate aberrations. It is characterized by excellent cross-polarization characteristics and tracking characteristics by higher-order modes without sacrificing the beam scanning characteristics of conventional torus antennas. Hereinafter, the present invention will be explained in detail with reference to Examples. FIG. 4 is a schematic diagram showing a first embodiment of a double-reflector antenna according to the present invention. The same reference numerals as in FIGS. 1 and 2 indicate the same parts as in FIGS. FIG. 4b shows a cross-sectional view in the yz plane of FIG. 4a. The antenna of this embodiment includes a main reflecting mirror 1, a sub-reflecting mirror 2, and a feeding horn 3.
The radio waves radiated from the feeding horn 3 are reflected by the sub-reflector 2, further reflected by the main reflector 1, and then proceed in the z direction to reach the aperture surface 7. The above configuration and operation are the same as those of the conventional antenna, but the main reflecting mirror surface of the antenna of this example is a cross-sectional curve 4 in the y-z plane designed according to the procedure described below.
It has a novel mirror surface obtained by rotating around the y' axis 5, which forms a constant angle with the y axis in the plane. In other words, in the conventional torus antenna, it is given by a parabola as shown by the broken line 4' in Figure 4b, but
The cross-sectional curve 4 according to the invention differs therefrom. The difference can be summarized as follows. If you extend the light ray from the main reflector to the sub-reflector, in the y-z plane, the conventional torus antenna shown by the wavy line will reach one point A.
On the other hand, in the antenna according to the present invention shown by a solid line, the antennas do not intersect at a single point. Below, a method for designing the mirror surfaces of the main reflecting mirror and the sub-reflecting mirror of the present invention will be explained in detail. In FIG. 4a, the phase center 6 of the feeding horn 3
Consider a cone 11 (for example, a cone) with the apex at The mirror surfaces of the main reflecting mirror 1 and the sub-reflecting mirror 2 are determined so as to satisfy the following conditions. The main reflecting mirror surface is a mirror surface rotated around the cross-sectional curve 4 with the y' axis 5 as the rotation axis. A straight line connecting points 14 and 15, parallel to the z-axis. Point 14 (and point 13) satisfies the law of reflection of light. No phase error occurs on the aperture surface 7. That is, the optical path length from the focal point 6 to the point 15 on the aperture surface is constant. A point 15 on the aperture plane lies on a desired mapping 16 (for example, a circle) on the aperture plane. Note that if the law of light reflection at point 14 and the above-mentioned condition of constant optical path length are satisfied, the law of light reflection at point 13 is naturally satisfied. A mirror surface that satisfies these conditions can be determined by solving differential equations as shown below. In the coordinate system shown in Figure 4 a or b, the origin 8
From the focal point 6 of the feeding horn, the point 13 on the sub-reflector,
The vectors up to point 14 on the main reflector are respectively
Let them be Fe, B, and M. Hereinafter, the symbol → represents a vector. The cross-sectional curve 4 of the main reflecting mirror is y′−
It is expressed as z′=f(y′) in the z′ coordinate system, and f′ is
Let df(t)/dt be expressed. Since the main reflecting mirror surface is a curved surface obtained by rotating the cross-sectional curve 4 about the y'-axis 5 as the rotation axis (the above condition), when the angle between the y'-axis and the y-axis is α, the vector M→ It can be expressed by the following formula. Note that the following matrix a b c represents ae→ _x +be→ _y +ce→ _z . However, e→ _x , e→ _y , and e→ _z are unit vectors in the x, y, and z directions, respectively. _{M → =} The unit normal n→ at point 14 on the main reflector is become. The light ray from the main reflecting mirror 1 to the aperture surface 7 is z
Since it is parallel to the axis (condition) and satisfies the law of reflection of light at point 14 on the main reflector (condition),
The unit vector s from point 14 on the main reflector to point 13 on the sub-reflector is s→=-k→+2(n→・k→)n→=1/1+f
′ ² −2 sin η (cos η cos α + f′ sin α) 2 (cos η cos α − f′ cos α) (cos η cos α + f′ sin α) 2 (cos η cos α + f′ sin α) ² − (1 + f′ ² ) ...(3). Here, k→ is a unit vector in the z direction. When the distance between points 14 and 13 is λ, vector B→ is given by B→=M→+λs→ ……(4). On the other hand, since the optical path length is always a constant length l ₀ (condition), λ and B→ satisfy the following equation. l ₀ =-z _n +λ+ |B→-F→ ₀ | =-z _n +λ+ |M→+λs→-F→ ₀ | ...(5) From equation (5), λ=1/2・(l ₀ +z _n ) ² −｜M/→−F/→ ₀ | ² /l ₀
+z _n +s·(M−F ₀ )...(6) is obtained. Vector B→ is obtained by substituting equation (6) into equation (4). Next, a polar coordinate system is set with the focal point 6 as the center and the direction from the focal point 6 to the point 10 as the zenith direction, and the angle from the zenith direction is θ, and the azimuth angle measured from the x-axis direction is taken. The vector from the origin to point 10 is B→ ₀
When, θ and are given by the following equations. cosθ=(B/→−F/→ ₀ )・(B/→ ₀ −F/→ ₀ )
/｜B−F ₀ |・|B ₀ −F ₀ |……(7) cos=i→・(B/→−F/→ ₀ /sinθ・|B−F ₀ | −B/→ ₀ −F /→ ₀ /tanθ・|B ₀ −F ₀ |)...(8) Here, i→ is a unit vector in the x direction. Using θ in such a polar coordinate system, the cone 11 whose apex is the phase center 6 of the feeding horn 3 is θ
and can be expressed as a function C(θ,)=O. For example, in the case of a right circular cone with half apex angle θ _b , C(θ, )=θ−θ _b =O (9). Also, the desired mapping 16 on the aperture plane 7 is x _n and
It can be expressed as a function of y _n H(x _n , y _n )=O. For example, a circle with radius ρ ₀ centered on the origin 8 can be expressed as H(x _n , _yn )=x _n ² + _yn ² −ρ ₀ ² =O (10). From equation (1), x _n and y _n are expressed by the variables t and η, so the function H becomes a function of t and η. Furthermore, by substituting the above equations (1), (3), and (6) into equation (4), vector B can be expressed using t, η, f, and f'. Therefore, from equations (7) and (8), θ is t, η,
It can be expressed by f and f', and C, which is a function of θ, can be expressed using t, η, f and f'. Next, by eliminating η from the above functions H and C, the functions of t, f(t) and df(t)/dt, that is, the ordinary differential equation of f(t) are obtained. A function f(t) is obtained by solving this ordinary differential equation.
Once the function f(t) is obtained, by substituting this function f(t) into the above equations (1) and (4), the main reflecting mirror 1
And the mirror surface of the sub-reflector 2 is determined. For example, cone 11 is a right circular cone in equation (9), and map 1
If 6 is the circle of equation (10), the differential equation is expressed by the following equation. f' ² (K ₂ H ₃ -H ₂ K ₃ ) + f' (K ₁ H ₃ -H ₁ K ₃ ) + (K ₀ H ₃ -H ₀ K ₃ )=O Here, K ₀ , K ₁ , K ₂ , K ₃ , H ₀ , H ₁ , H ₂ and H ₃ are given by the following equations. K ₀ = l ₀ + F _z +2 (cos η cos ² α + sin ² α) × {sin η
cosαx _n +sinαcosα (cosα-1)(y _n −F _y )+(cosηcos ² α＋sin ² α)
(z _n +F _z )} K ₁ =2x _n sinηsinα{2(cosη-1)cos ² α+1}−2(
y _n −F _y ) {cosη+2(cosη-1) ² sin ² αcos ² α}−4(z _n −F _z ) sinαcosα(cosη
-1)(cosηcos ² α+sin ² α) K ₂ =l ₀ +F _z −2sinαcosα(cosη−1) {sinηsin
αx _n −(sin ² αcosη+cos ² α) (y _n −F _y ) −(cosη−1)cosαsinα(z _n −F _z )} K ₃ = 1/2 {(l ₀ +z _n ) ² −x _n ² −(y _n −F _y ) ² −(z
_n −F _z ) ² } H ₀ = −cosθ _b +cosθ ₀ −2(cosηcos ² α+sin ² α){cos
ηcosαcos(θ ₀ -α)-sinαsin(θ ₀ -α)} H ₁ =2sinθ ₀ (cosηcos ² α+sin ² α)+2sinα(cosη-1)
{2cosηcos(θ ₀ -α)cos ² α+sinαsin(2α-θ ₀ )} H ₂ =−cosθ _b +cosθ ₀ −(cosη-1)sin2α{cosηsinα
cos(θ ₀ -α)+cosαsin(θ ₀ -α)} H ₃ =−cosθ _b・(l ₀ +z _n )+(y _n −F _y ) sinθ ₀ + (
z _n −F _z ) cosθ ₀ However, η＝cos ⁻¹ {sinα(t・cosα−f(t)sinα)+
√f ² (t) + t ² −ρ ₀ ² /cosα(f(t)cosα+t・si
nα)} F→ ₀ = O F _y F _z . Further, θ ₀ represents the angle between the direction from point 6 to point 10 and the z-axis. This differential equation can be easily solved using an electronic computer. Next, a specific example of a mirror surface synthesized by the above design method will be shown. In this specific example, when creating a mirror surface, initial conditions are set as follows. C(θ,)=θ−15.33゜H(x _n , y _n )=x _n ² +y _n ² −(0.15) ² =O θ ₀ =O α=O l ₀ =1.572 However, the coordinates of point 9 are (O, O, -1) The coordinates of point 10 are (O, -0.263, -0.737) The coordinates of point 6 are (O, -0.263, -0.937) Under the above initial conditions, the cross-sectional curve of the main reflector 4
The coordinates (O, y _n , z _n ) of are determined as shown in Table 1.

[Table] FIG. 5 shows the calculation results of the radiation directivity of the antenna constituted by the cross-sectional curve 4 shown in FIG. 4b obtained according to the present invention. Similar to FIG. 3, this figure shows the shape of the antenna beam using equilevel lines, and assumes that the directivity of the feeding horn 3 is a circular beam as shown in FIG. 3b. In this case, the antenna beam is almost circular without distortion as shown in FIG. 3a. In the antenna of this embodiment formed as described above, when beam scanning is performed in the xz plane, the y' axis and the y axis may be aligned. Also,
When this antenna is used as an earth station antenna for fixed satellite communication, the angle between the y' axis and the y axis can be determined from the latitude of the earth station, and beam scanning can be performed along the satellite orbit. In this case, the angle does not exceed 10°, for example approximately 4° for an earth station located at 30° latitude. In addition, in the antenna of this embodiment, by using a mirror surface in which the mapping 16 on the aperture plane is centered at point 8 and becomes an ellipse long in the x-axis direction, the antenna beam becomes an ellipse long in the direction perpendicular to the satellite orbit. is obtained, and a simple method that omit tracking in this direction is also conceivable. Although the ring of the main reflecting mirror 1 is drawn in a rectangular shape in FIG. 4a, this is not essential and may be circular or elliptical. FIG. 6 shows an example of application in which the multi-reflector antenna of the present invention is used as a multi-beam antenna. Since the main reflecting mirror 1 is a rotating body with the y'-axis 5 as the rotation axis, the feeding horn 3 and the sub-reflecting mirror 2 are placed in a position rotated around the y'-axis while maintaining their positional relationship. By fixing these,
Optically, a plurality of antenna beams can be configured without any change in characteristics. for example,
Sub-reflector 2, 2', 2'' and feeding horn 3, 3',
3" may be arranged in pairs as shown in the figure. Also, these feeding horns 3, 3', 3" and sub-reflectors 2, 2', 2" may be moved around the y' axis. Accordingly, it can also be used as a beam-shifting multi-beam antenna.Another application example of the present invention is shown in Fig. 7.The main reflector 1 and the sub-reflector 2 are the same as in the previous embodiment. The mirror surfaces 17 and 18 are two parabolic mirrors of revolution with parallel axes of rotation designed in the same way as before, and the light rays are focused at a focal point 6. The light beam emitted from the main reflector 6 is again focused on the next focal point 19. The focal point 19 is located on the rotation axis 5 of the mirror surface of the main reflecting mirror, and the feeding horn 3 is arranged so that its center axis coincides with the axis 5. In this application example, a beam feeding reflector using a sub-reflector 2 and two parabolic mirrors 17 and 18, that is, a portion A surrounded by a dotted line in FIG. By rotating around , it is possible to scan the antenna beam over a wide angle while fixing the positions of not only the main reflector 1 but also the feeding horn 3. As described above, the double reflector antenna according to the present invention According to the method, there is an effect that the shape of the antenna radiation beam can be shaped.Furthermore, in the antenna according to the present invention, by rotating the sub-reflector and the wave source around the rotation axis of the main reflector, the main reflector can be shaped. This has the advantage of being able to scan a fixed shaped antenna beam without deteriorating its characteristics, and also providing a multi-beam antenna that can shift the beam.Furthermore, the shape of the feeding horn's radiation beam and the radiation beam of this antenna can be Since the shapes can be made almost similar, there is also the effect that cross polarization characteristics and tracking characteristics by higher-order modes can be improved.The antenna according to the present invention has the above-mentioned effects, so Effective for large-diameter antennas of satellite communications earth stations.

[Brief explanation of drawings]

1 and 2 are block diagrams showing specific examples of conventional torus antennas, FIG. 3 is an explanatory diagram for explaining the radiation directivity of the conventional torus antenna, and FIG. FIG. 5 is a radiation directivity diagram of a double-reflector antenna according to the present invention, and FIGS. 6 and 7 are configuration diagrams showing application examples of the present invention. 1... Main reflecting mirror, 2... Sub-reflecting mirror, 3... Feeding horn, 4... Cross-sectional curve of main reflecting mirror, 5... Axis,
6...Phase center, 7...Aperture plane, 8...Origin, 1
1...cone, 12...ray, 16...mapping.

Claims (1)

[Claims] 1. In a multi-reflector antenna having a main reflector made up of a part of a rotationally symmetrical surface, at least one sub-reflector, and at least one wave source, coordinates with the origin placed on the aperture plane Using a system, when the vector from the origin to the mirror surface of the main reflecting mirror is M→, and the vector from the origin to the mirror surface of the sub-reflecting mirror is B→,
The vectors M→ and B→ are expressed by the following equations (1) and (2), respectively.
and f(t) in equations (1) and (2) define a radio wave path passing through one closed curve C ₁ on the aperture of the wave source and one closed curve C ₂ on the antenna aperture. A multi-reflector antenna comprising a main reflector and a sub-reflector that are substantially determined by the solution of a differential equation created under the condition that the radio wave paths are matched. M→=−f(t) sinη f(t) cosηsinα+tcosα f(t) cosηcosα−tsinα ……(1) B→=M→+λs→ ……(2) However, s→=1/1+f′(t) ^2−2sinη (cosηcos
α+f′(t)sinα) s→=1/1+f′(t) ² −2sinη(cosηcos
α+f′(t)sinα) 2(cosηsinα−f′(t)cosα)(cosηcosα+f′
(t) sinα) s→=1/1+f′(t) ² −2sinη(cosηcos
α+f′(t)sinα) 2(cosηsinα−f′(t)cosα)(cosηcosα+f′
(t) sinα) 2 (cosηcosα+f′(t) sinα) ² −(1+f′(t)
² ) λ=1/2・(l ₀ +f(t)cosηcosαts
inα) ² −｜M/→−F/→ ₀ | ² /l ₀ +f(t)cosηco
sα−tsinα+s・(M−F ₀ ) Here, t and η are parameters representing the curved surface,
α is the angle between the rotation axis of the main reflector and the antenna aperture, l ₀ is the radio wave path length from the wave source to the antenna aperture via the secondary and main reflectors, and F→ ₀ is the vector from the origin to the focal point of the feeding horn. , f'(t) is df(t)/dt. 2. The multi-reflector antenna according to claim 1, wherein the closed curve C ₁ and the closed curve C ₂ are similar. 3. The first claim, wherein the closed curve C ₁ is a circle, and the closed curve C ₂ is an ellipse.
Multi-reflector antenna described in section.