I. A. Kuznetsov1, A. N. Gribanov2, G. F. Moseychuk3, A. I. Sinani4
1–4 JSC “V. Tikhomirov Scientific Research Institute of Instrument Design” (Zhukovsky, Russia)
Antenna systems with electronic beam control can include both one and several phased antenna arrays. Their apertures can be located at different angles relative to any selected direction, for example, the construction axis of the carrier.
Each phased antenna array with a flat aperture has a two-dimensional angular region θ ≤ 90°, in which the angles θ are counted relative to the normal to the aperture. This area is called the front hemisphere or the field of view of the antenna. At the same time, phased antenna arrays are characterized by the size of the angular scanning area, which, as a rule, does not exceed ±60°. It is also important to know the location of the single-beam scan zones, which should generally be located outside the scan area. The basic radiation characteristics of each individual phased antenna array are most easily represented in their own coordinate system of the guiding cosines (u, v) to the orthogonal axes of the aperture (u = sinθ cosφ, v = sinθ sinφ). In this case, the field of view is limited by the circle r = sqrt(u2 + v2) = 1. In this paper, we assume that the scanning area of each phased antenna array is bounded by a circle with a radius r = sin(60°) ≈ 0,87. The boundaries of the single-beam scanning zones are parts of circles of unit radius, the centers of which are located outside the field of view. In the proper coordinate system, the Azimuth-Elevation (Az, El), the field of view of each phased antenna array has the shape of a square with sides of ±90°. The shape of the boundaries of the scanning area and singlebeam zones is also due to the transformation of coordinate systems. To represent the directional characteristics of the entire antenna system, which includes several multidirectional phased arrays, in the angular space of the carrier, the mathematical apparatus and the corresponding mathematical modeling program in the Matlab environment have been developed.
The mathematical apparatus of rotations of coordinate systems in three-dimensional space includes the use of Euler angles. In general, the rotation of the coordinate system is reduced to three particular rotations around the axes of the rectangular coordinate system XYZ. To determine the new position of the point {x2, y2, z2} in space, the former coordinates of the point {x1, y1, z1} must be multiplied by the conversion matrix. Multiplying the coordinates of a point during rotation is carried out sequentially: the coordinates of the point are multiplied by the final conversion matrix or by each of the three matrices that take into account rotation around their axes. At the same time, it is necessary to strictly observe the order of operations that are uniquely related to the sequence of rotations. Calculations and representations of the boundaries of the field of view and scanning are convenient to use if the antenna system includes several phased antenna arrays located at different angles relative to the selected axis of the object.
In this paper, we have considered the issues of displaying the areas of visibility and scanning of all the antennas that are parts of the selected antenna system. Combining the scanning areas of all antennas into a single coordinate system associated with the support on which the antenna system is installed allows you to get information about providing a view of the space, the presence of blind spots and other characteristics of antenna devices. Such analysis of an antenna system consisting of several antenna devices will allow you to simulate the antenna system at an early stage and make adjustments to the location of the antennas on the support in order to maximize their use.
Kuznetsov I.A., Gribanov A.N., Moseychuk G.F., Sinani A.I. Simulation of characteristics of the antenna system consisting of plane phased array antennas. Antennas. 2021. № 5. P. 46–51. DOI: https://doi.org/10.18127/j03209601-202105-05 (in Russian)
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