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Realization algorithm of the given amplitude distribution on a plane antenna array with triangular structure of the radiator’s placement

Keywords:

V.A. Voloshin, A.Yu. Larin, A.V. Litvinov


An iteration algorithm has been formulated for calculating the row and column factors providing the given equivalent amplitude distributions along the axes OX and OY of the plane antenna array (PAA) with the triangular structure of the radiator’s arrangement. As given distributions we choose the known amplitude ones of the two equidistant linear antenna arrays, the radiator’s number in which coincides with the number of columns and rows of the plane aperture respectively. Iterative algorithm is based on the account of a certain number of rows and columns of plane aperture with the triangular structure of the radiator’s placement. In this case, the number of columns and rows can be either even or odd. The algorithm consists of the following steps: as initial approximations of the desired column and row amplitude factors we choose known amplitude distributions of the two linear antenna arrays, for example of the cosine-square form on the pedestal; PAA with a triangular radiator’s structure is divided into two with the rectangular structure of the radiator arrangement. First antenna array consists of columns and rows with odd numbers, and the second array – columns and rows with even numbers; from two preassigned amplitude distributions the coefficients with the odd x (row-1) and y (column-1) are chosen for the first antenna array, and even terms for x (row-2) and y (column-2) for the second one; iterative procedure for each antenna array with rectangular structure of the radiators begins with defining the sum of the column radiator amplitudes; the new row amplitudes are obtained by dividing into sums of the column amplitudes and normalized to the maximum value; the sums of the new row radiator amplitudes are determined; the new column amplitudes are obtained by dividing into sums of the row amplitudes and normalized to the maximum value; taking into account that the amplitude of each radiator equals the product of the row and column amplitudes we calculate the amplitude distributions of the two equivalent linear antenna arrays of the plane aperture (the projections of the radiator amplitudes of the plane aperture on the axis OX and OY) and define the maximum deflections of the realized equivalent and given amplitude distributions along the two orthogonal axes of the plane aperture. The run out from the iteration procedure occurs in the case when two maximum deflections are less than some minor magnitude eps = 10-9. Eight iterations are sufficient for the majority versions of the decreasing amplitude distributions; the even and odd terms of row and column of the factors of two antenna arrays with rectangular structure are combined into row and column of the original factors antenna array with triangular structure; the deviations of realized equivalent and given amplitude distributions on two orthogonal axes of the plane of the aperture of the original antenna array with a triangular structure are calculated. The results of amplitude distributions calculation are presented for the three variants of the aperture geometry, demonstrating the ability of the algorithm.
References:

  1. Voloshin V. A., Larin A. Ju., Ovodov O. V. Realizacziya zadannogo amplitudnogo raspredeleniya na ploskom raskry've FAR s proizvol'noj formoj graniczy' // Antenny'. 2009. № 9 (148). S. 12 – 16.
  2. Strizhkov V. A. Napravlenny'e svojstva i uroven' bokovogo izlucheniya slabovy'pukly'x fazirovanny'x antenny'x reshetok // Antenny'. 2007. № 1. S. 7 – 27.
  3. Voloshin V. A., Larin A. Ju., Ovodov O. V. Algoritm sinteza linejny'x antenny'x reshetok po zadannoj ogibayushhej bokovy'x lepestkov diagrammy' napravlennosti // Antenny'. 2011. № 12(175). S. 3 – 7.
  4. Markov G. T., Sazonov D. M. Antenny'. M.: E'nergiya. 1975. S. 308 – 310.

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