OFFSET-FED DUAL REFLECTOR ANTENNA

Abstract: An offset-fed dual reflector antenna comprising a main reflector (3) and a sub-reflector (2) and a primary radiator (1) which do not block the wave-path of the main reflector is improved by inclining the primary radiator relative to the boresight axis of the antenna. The main reflector and/or the sub-reflector has a quadratic surface to provide a desired aperture field distribution, improved cross-polarization characteristics, and improved side­ lobe characteristics. The slant angle of the primary radiator is in the range from 10 degrees to 40 degrees. If a gregorian antenna is used, and the aperture field distribution is a Taylor's - 40 dB distribution, the slant angle is preferably 16 degrees.

Description: This invention relates to an offset-fed dual-reflector antenna the main reflector and sub-reflector of which are shaped in a non-quadratic surface. An offset-fed dual-reflector antenna has the feature that its primary radiator and sub-reflector do not cover the aperture of its main reflector. Therefore, the antenna gives no unnecessary electromagnetic wave scattering and has an excellent wide angle radiation directivity. For this reason it has been in practical use in the communications field and in radar applications. A conventional Cassegrain antenna of the axial symmetry type in which the sub-reflector is not offset has the advantage of obtaining an ideal directivity by modifying the electric field distribution at the aperture to a desired distribution with shaped non-quadratic surfaces of the reflectors. On the other hand, an offset-fed dual-reflector antenna has no design freedom to choose a desired electric field distribution at the aperture, and this is considered a great drawback of an offset-fed dual reflector antenna. This is due to the following reasons. When the reflector system of an offset-fed dual-reflector antenna is determined by numerical calculation, in general the following three conditions must be satisfied. 1) The optical path length from the phase centre of the primary radiator to the aperture plane is constant for every optical path. 2) The reflection law (the incidence angle of the input beam is equal to that of the output beam) is satisfied at the sub-reflector. 3) The reflection law is satisfied at the main reflector. In addition to the above three conditions, the following condition is necessary for obtaining a desired electric field distribution in the radial direction of the aperture. 4) An energy distribution condition in the radial direction (the field distribution on the aperture plane). Furthermore, for an excellent cross polarization characteristic, the following condition is required. 5) The electric field distribution at the aperture in the circumferential direction is symmetrical about the axis. An analytical solution satisfying the above five conditions simultaneously is, however, impossible because no such solution exists, and this is the main reason for the drawbacks. For example, a particular kind of offset-fed dual-reflector antenna, as disclosed in Japanese Patent Application No. 34652/76 "Antenna of an offset aperture type", has a reflector system satisfying conditions 1), 2), and 3), and the electric field distribution at the aperture is of axial symmetry because the condition 5) is introduced to suppress the generation of cross polarization components. As a result, the electric field distribution in the radial direction is automatically predetermined, because the reflector system is determined completely by the four conditions and there is no room for applying condition 4). Hence, a desired field distribution on the aperture plane cannot be implemented. Therefore, the directivity of an antenna of this kind cannot be optimized to the associated radio circuitry, and the said drawbacks of an offset antenna still remain unsolved in this design method. Another conventional approximation method has been proposed to provide a desired electric field distribution at least in the vertical plane of a reflector (see Japanese Utility Model Application No. 19853/83). In this method, in the first place, only the vertical central cross section curves of the offset-fed dual-reflector antenna are obtained under the above-mentioned conditions 1), 2), 3), and 4). Then, it is assumed that the surface of the sub-reflector and the main reflector comprises a group of ellipses the long axis of which exists on the plane obtained by connecting two points of the corresponding cross section curve. Next, the rest of the coordinates, other than those of the cross section curve, are determined by applying the conditions 1) and 2) only. Further, an approximation for the condition 5) is obtained by setting the angle between the primary radiator and the sub-reflector properly. US Patent 3792480 describes an aerial system in which the sub-reflector and main reflector are part hyperboloid, part paraboloid respectively. The surface profile of this quadratic surface antenna is determined from focal length and eccentricity, but the use of quadratic antenna generates a cross polarization component on the aperture plane which is minimized by a properly designed slant angle of the primary radiator. Suppressing the cross polarization component has the effect of making the bore sight jitter and frequency sensitive squint become small. Accordingly, in this method, a desired electric field distribution is established only in the portion of the vertical central cross section curve and its vicinity, and in other portions of the reflector surface the condition 4) is not satisfied. Generally, an antenna for use in a microwave relay circuit is expected to have an excellent wide angle radiation directivity in the horizontal plane. As the electric field distribution in the horizontal direction is directly related to the directivity, this design method, which does not give a desired electric field distribution in the aperture in the horizontal direction, is not suitable for antennas for that purpose. Considering the antenna design methods stated above, a new design method has been proposed where the central axis of the primary radiator is set parallel to the antenna's main radiation direction (boresight axis), and the reflector surface coordinates are calculated under the above-mentioned conditions 1), 2), 4), and 5). (See Lee, Parad, Chu, "A Shaped Offset-Fed Dual-Reflector Antenna", IEEE trans. on AP, AP-27, 2, pp.165/171, March 1979). In this method, however, as the condition 3) is completely ignored and the condition 2) is not considered adequately, an electromagnetic wave which is reflected by the main reflector and propagates toward the main radiation direction has variations in the direction of its components. Furthermore, as this directional error varies in magnitude and direction from one point to another of the aperture, the total electromagnetic wave does not converge correctly. In a case where the size of the antenna's aperture is not so large compared with the wave length of the electromagnetic wave, the influence of this effect on the co-polarization characteristic can be neglected. However, it brings about a serious deterioration of the cross polarization characteristic because of the antenna's design based on the condition 4). Also, when the size of the aperture is larger than 100 times the wavelength, the influence of this effect on the co-polarization characteristic can no longer be ignored. It is an object of the present invention to provide a new and improved dual reflector antenna which, in a practical sense, satisfies the above conditions 1), 2), 3), 4), and 5). According to the invention there is provided an offset-fed dual reflector antenna comprising a main reflector, a sub-reflector, and a primary radiator, the sub-reflector and the primary radiator not blocking the wavepath of the main reflector, characterized in that the surface of the main reflector and the sub-reflector are non-quadratic being determined so that the optical path length between the phase centre of the primary radiator and the aperture plane is constant, the law of reflection at the sub-reflector is satisfied, and the field distribution in the aperture plane of the antenna is symmetrical about the axis, characterised in that the primary radiator is positioned so that it is slanted from a line parallel to the boresight axis of the antenna by an angle which gives minimum directional error of the antenna from the boresight axis, when the desired field distribution on the aperture plane is provided. An embodiment of the invention will now be described, by way of example, with reference to the accompanying drawings, in which Figure 1 is a simplified diagram of an antenna configuration of the invention for explaining the principle of the invention; Figure 2 is a graph for explanation of the effect of inclining the central axis of the primary radiator; Figure 3A and Figure 3B show curves for selecting an optimum slant angle of a primary radiator in the present invention; Figure 4 shows curves representing the cross sections of components in an embodiment of the invention; Figure 5 is a graph of a theoretical radiation characteristic of the embodiment of Figure 4; and Figure 6 is an end elevation of the structure of an antenna according to the invention. Figure 1 shows a simplified diagram for explanation of the principle of an antenna according to the present invention. The antenna comprises a primary radiator 1, a sub-reflector 2, and a main reflector 3. The primary radiator 1 has a phase centre at the origin 0 of a rectangular coordinate system X-Y-Z, and the primary radiator 1 has a central axis on the X-Z plane making an angle δ with the Z axis, which coincides with the boresight axis of the antenna. The primary radiator 1 has a power directivity in the ϑ direction given by W p (ϑ), while that in the  direction is of axial symmetry. Such a directivity can be realized by means of a corrugated horn or the like. The reflector surface coordinates of the sub-reflector 2 are represented by a spherical coordinate system (r, ϑ, ) the origin of which is the said origin 0, whilst the reflector surface coordinates of the main reflector 3 are represented by a cylindrical coordinate system (z, ρ, ψ) the origin of which is chosen as X m1 (X m1 , 0, 0). The radiation direction (boresight axis) of the antenna is in the Z axis direction. A desired power distribution at the aperture is denoted by W a (ρ). That is, the power varies as specified by W a (ρ) from the central axis of the aperture to its radial direction, whilst in the ψ direction the power distribution is of axial symmetry. As stated earlier, in order to obtain the reflector system of the antenna shown in Figure 1 by numerical calculation, first of all the following three conditions are necessary. 1) The optical path length from the phase centre of the primary radiator to the aperture is constant. 2) The reflection law holds at the sub-reflector 2. 3) The reflection law holds at the main reflector 3. The reflection law says that the incidence angle of the input beam is equal to that of the output beam. In addition, the conditions 4) and 5) are expressed as follows, respectively. 5) ϑ o = ψ (2) where ϑ o is the angle between the central axis of the primary radiator 1 and any point on the edge of the sub-reflector 2, W p (ϑ) is the power directivity of the primary radiator and ρ o is the radius of the aperture. As stated above, it is impossible to get an analytical solution which satisfies the five conditions simultaneously. This invention provides the following method which makes it possible to get a solution where the five conditions are satisfied in a practical sense. In the first place, by solving the four conditions 1), 2), 4), and 5) simultaneously, the reflector surface coordinates of the main reflector and the sub-reflector are calculated, where the central axis of the primary radiator is assumed to make a constant angle δ with the Z axis at the origin. This calculation is conventional, and is implemented and explained in the above-mentioned article by Lee, Para and Chu. In this state of the reflector system, as the condition 3) is not taken into consideration, an electromagnetic wave radiated from the reflector system does not propagate in the Z axis direction but has some directional error. That error is compensated by the slant angle of the primary radiator. Accordingly, the slanted primary radiator is an important feature of the present invention. The path traced by an electromagnetic wave which is radiated from the primary radiator, reflected at the sub-reflector in accordance with the reflection law, and then reflected at the main reflector in accordance with the reflection law is calculated by means of geometrical optics. The directional error in this case is the angle between the actual direction of the path after the reflection at the main reflector and the Z axis. When the slant angle of the primary radiator is taken as a parameter, and the path for each reflector surface coordinate is calculated in turn, the directional error for each slant angle of the primary radiator changes in absolute value. This is shown in Figure 2 where the x axis and the y axis are calibrated in slant angle (δ) and magnitude of directional error, respectively. The magnitude of the directional error depends on the point in the aperture. In general, the nearer the point to the centre of the aperture, the smaller is its directional error value, and so the range of directional error for each particular slant angle (δ) is indicated by a vertical short line in Figure 2. In Figure 2, the power directivity of the primary radiator is approximated by cosine to the power n, and W p (ϑ) = cos 99.63 (ϑ/15) (3) is assumed so that -15 dB is provided when ϑ = 15°. The power distribution at the aperture is also assumed as follows. The above expression is a distribution of the low side lobe type known as a Taylor distribution (Taylor's -40 dB distribution). As seen from Fig.2, there is an optimum value of slant angle δ. In this case, the directional error becomes nearly zero at δ = -16.53°. This optimum value of δ depends on W p , W a , and the offset angle γ. If W p is as given by equation (3), Figs.3A and 3B are obtained for each offset angle γ between the path reflected by the sub-reflector and the Z axis. In Figs.3A and 3B, the x axis and the y axis are calibrated in offset angle γ and optimum slant angle δ, respectively, with the aperture distribution type taken as a parameter, where the offset angle γ is defined as the angle made by the line obtained by connecting the centre of the main reflector and that of the sub-reflector, and the YZ plane. In Figs.3A and 3B the curve (a) shows the case of "uniform distribution" where the electric intensity is uniform over the aperture, i.e. it is a distribution of the so-called high efficiency type. The curve (b) shows the case of (1-ρ²) distribution, the curve (c) shows the case of (1-ρ²)² distribution, and the curve (d) shows the case of Taylor's -40 dB distribution. The (1-ρ²)² and the Taylor's -40 dB distribution curves are both of the low side lobe type. Fig.3A shows the case where the antenna is a gregorian antenna which has a sub-reflector with a concave surface, and Fig. 3B shows the case where the antenna is a cassegrain antenna which has a sub-reflector with a convex surface. It should be noted in Fig.3A that the optimum slant angle δ is 16.53° (absolute value) for Taylor's -40 dB distribution, for the offset angle γ = 60°. Also, in Fig.3A, the preferable slant angle is 12° (absolute value) for uniform distribution, when the offset angle is 60°. In case of a cassegrain antenna, as shown in Fig.3B, the preferably slant angle for Taylor's -40 dB distribution is 18° when the offset angle is 60°, and the preferable slant angle is 14° for uniform distribution when the offset angle is 60°. As is clear in Figs.3A and 3B, the optimum slant angle is negative when the sub-reflector is concave, and is positive when the sub-reflector is convex. Of course, the present idea is applicable to a wide range of distribution types besides those shown in Figs.3A and 3B. As explained above, in the present invention the slant angle of the primary radiator is first set to the optimum value as shown in Figs.3A and 3B, and the reflector surface coordinates are calculated by the method explained earlier, so that an electromagnetic wave reflected at the entire surface of the main reflector propagates in the direction of the Z axis with negligible directional error. Then the condition 3) (the reflection law at the main reflector) and the condition 4) are satisfied in practice. Fig.4 illustrates the cross sectional shapes of an embodiment of the invention, where the curves 1, 2 and 3 indicate the cross sections of the primary radiator, the sub-reflector, and the main reflector, respectively. The scales of the x axis and the y axis are normalized by wave length, and W p , W a are equal to those in the equations (3) and (4), respectively. Furthermore, it is assumed that γ = 60°, δ = -16.53°. Fig.5 shows a theoretical radiation characteristic of the embodiment shown in Fig.4. This is the directivity in the horizontal plane by vertical polarization transmission, where the directivity of vertical polarization is shown in a solid line and that of horizontal polarization or cross polarization is shown by a dotted line. The first side lobe level (in the solid line) and the maximum value of cross polarization lobe (in the dotted line) are given by -37 dB and -42 dB, respectively, which are low enough for practical purposes. This indicates the excellent characteristics of an offset-fed dual reflector antenna according to the present invention. Fig.6 shows an experimental structure of a cassegrain antenna according to the present invention. The structure comprises a primary radiator 1, a sub-reflector 2, a main reflector 3, frames 12a-12k, pins 14 for fixing the main reflector to the frame 12a, a mounting frame 16, and a waveguide 18 for feeding the primary radiator. It should be appreciated that the present invention is applicable to both a gregorian type antenna and a cassegrain type antenna. As explained above, in designing an offset-fed dual-reflector antenna, if the central axis of the primary radiator is slanted relative to the radiation direction of the antenna by a constant angle, and the reflector surface coordinates of the main reflector and the sub-reflector are obtained so that the electric field distribution of the aperture is specified by a particular function in the radial direction from the centre of the aperture, keeping axial symmetry in the circumferential direction, the electromagnetic wave reflected at the main reflector propagates in the boresight axis direction with small directional error. Therefore, a desired aperture distribution can be realised with little deterioration of the efficiency of the aperture and the cross polarization characteristic. In addition, if the angle initially slanted is set to an optimum value, the directional error becomes almost zero. That is, the electric field distribution of the aperture can be as desired in the radial direction, while it is of axial symmetry in the circumferential direction with all the design conditions of the reflector system satisified. That is, the invention realizes an offset-fed dual-reflector antenna with an ideal co-polarization directivity and excellent cross polarization characteristics.

Claims: An offset-fed dual reflector antenna comprising a main reflector (3), a sub-reflector (2), and a primary radiator (1), the sub-reflector and the primary radiator not blocking the wavepath of the main reflector, characterized in that the surface of the main reflector and the sub-reflector are non-quadratic and are determined so that the optical path length between the phase centre of the primary radiator and the aperture plane is constant, the law of reflection at the sub-reflector is satisfied, and the field distribution in the aperture plane of the antenna is symmetrical about the axis; and in that the primary radiator is positioned so that it is slanted from a line parallel to the boresight axis of the antenna by an angle which gives minimum directional error of the antenna from the boresight axis, when the desired field distribution on the aperture plane is provided. An antenna according to claim 1, characterised in that the absolute value of the slant angle of the primary radiator (1) is between 10° and 40°. An antenna according to claim 2, characterised in that the slant angle of the primary radiator (1) is approximately 16°; and the antenna is a gregorian antenna which has a sub-reflector (2) with a concave surface, with an offset angle of 60°, to provide a Taylor's -40 dB distribution on the aperture plane. An antenna according to claim 2, characterised in that the slant angle of the primary radiator (1) is approximately 12°; and the antenna is a gregorian antenna which has a sub-reflector (2) with a concave surface, with an offset angle of 60°, to provide uniform distribution on the aperture plane. An antenna according to claim 2, characterised in that the slant angle of the primary radiator (1) is approximately 14°; and the antenna is a cassegrain antenna which has a sub-reflector (2) with a convex surface, with an offset angle of 60°, to provide uniform distribution on the aperture plane. An antenna according to claim 2, characterised in that the slant angle of the primary radiator (1) is approximately 18°; and the antenna is a gregorian antenna which has a sub-reflector (2) with a concave surface, with an offset angle of 60°, to provide a Taylor's -40 dB distribution on the aperture plane.

Inventors: KAGOSHIMA, KENICHI, KARIKOMI, MASAHIRO
Applicants: NIPPON TELEGRAPH AND TELEPHONE CORPORATION
Application year: 1985
Main classification: H01Q19
IPC codes: H01Q19, G02B5