Electrodynamic analysis of ring array of vertical asymmetric vibrators

The key task of constructing stationary ground stations for information exchange via an ionosphere channel is to develop antenna systems which provide high spatial-frequency selectivity of transmitting and receiving signals with seasonal and daily fluctuations of electrophysical parameters of the propagation medium. An effective solution to this problem is based on the use of vertical asymmetric vibrators placed on the earth's surface on concentric circles as transmission and reception structures of arrays. The selected array configuration allows for a circular view of the space with a high directional coefficient under deployment area constraints within the transceiver station. The annular structure, which preserves the invariance of the structure when rotating in the azimuth plane around the central longitudinal axis at an angular distance between the vibrators, provides a circular view of the space with a high coefficient of directional action. The placement of antenna elements on several rings with a common center contributes to the expansion of the frequency range for scanning space compared to a single ring system with restrictions on the occupied area. Rational versions of arrays are established on the basis of electrodynamic analysis of relationships between parameters of structures and characteristics of signal transmission and reception. The purpose of the article is to establish patterns of change in directional properties of arrays with various electrical dimensions, the number of antenna elements and concentric circles. Using the apparatus of Hallen integral equations and the Krylov–Bogolyubov numerical method, electrodynamic analysis of ring arrays of vertical asymmetric vibrators for stationary terrestrial transmission and reception posts has been carried out to solve them. Setting of the boundary problem has been performed with application of principle of mirror images from flat platform, chosen for array rotation on earth surface, which has properties of ideally conducting material in the range of ionosphere propagation wavelengths. A system of integral equations with nuclei in the form of Green functions for point emitters in a homogeneous isotropic infinitely long medium relative to equivalent array currents has been obtained from the condition of turning to zero the tangential components of the superposition of intrinsic electric fields on the surfaces of vibrators and their equality to vertical projections of fields created by generators of electromotive forces in gaps for connecting outputs of a distribution line. According to results of numerical solution of integral equations by conversion to system of linear algebraic equations for calculation of complex amplitudes of equivalent currents of antenna elements at the approximation by sequences of piecewise constant basic functions, spatial-frequency selectivity of transmission-reception by arrays with certain parameters of structures has been investigated. Distribution of array currents is restored by summation of sequences of piecewise constant basis functions with specified weight coefficients found at partial inversion of matrix operator and control of achievable accuracy of calculations by residual error of boundary conditions of a boundary problem. Laws of change of array directivities at various electric dimensions, number of vibrators and density of their arrangement on concentric circles have been revealed. On the basis of electrodynamic analysis, relationships of characteristics and parameters of structures of ring arrays of vertical asymmetrical vibrators located on infinitely extended perfectly conducting flat surface have been established. Possibilities of increase of spatial-frequency selectivity of signals transmission-reception when propagating along ionosphere channel have been investigated. When the generators of external electromotive forces are included in the final axial breaks of the elements, the effective receiving-emitting surfaces of the vibrators decrease, the absolute values of currents decrease in comparison with the values achieved when excited by point sources of high-frequency oscillations. To increase the directivity of the array with a distribution line to a value achievable when excited by ideal sources in infinitesimal axial gaps, it is necessary to increase the lengths of the vibrators by the width of the gap. The obtained results make it possible to justify rational design alternatives of antenna arrays when simultaneously fulfilling tactical and technical requirements for functional properties and maximum permissible dimensions for deployment with stationary ground transceiver stations.