A.R. Bestugin – Dr.Sc. (Eng.), Professor, Director of Institute of Radio Engineering, Electronics and Communication,
Saint-Petersburg State University of Aerospace Instrumentation
A.N. Yakimov – Dr.Sc. (Eng.), Professor, Saint-Petersburg State University of Aerospace Instrumentation
I.A. Kirshina – Ph.D. (Econ.), Associate Professor, Saint-Petersburg State University of Aerospace Instrumentation
A.V. Nerobeev – Post-graduate Student, Saint-Petersburg State University of Aerospace Instrumentation
In the ground radio line of communication electromagnetic waves propagate in close proximity to the earth's surface, interacting with it. This leads to the formation of a complex spatial structure of the electromagnetic field, which must be taken into account when designing such radio lines. The mathematical model of the ground radio line of communication should take into account the spread of both «direct» and reflected from the earth's surface radio waves. In the microwave range, the mathematical model of the radio line of communication be based on the calculated expressions obtained using the methods of geometric and physical optics. One of the main problems is to assess the influence of antennas on the characteristics of the ground radio line of communication. A promising direction in this study is the representation of antennas and other objects in the form of spatially distributed structures. The proposed mathematical model of the ground radio line of communication allows to estimate the influence of the antennas used on the characteristics of the radio line and to determine their optimal size and spatial location. In the construction of a mathematical model of the ground radio line of communication for the correct solution of the electrodynamic problem, the following assumptions are made: the earth's surface is flat and perfectly smooth, electromagnetic waves are monochromatic, created and propagated in a linear, homogeneous and isotropic environment with low conductivity in the absence of external sources of the field.
The classical approach to the summation of «direct» and reflected waves by the method of geometrical optics, despite the good agreement of theoretical and experimental results, does not allow to take into account all the processes in detail. More accurately considered processes can be described by the method of wave optics. As a result, it is possible to construct a mathematical model, where the signal received by the receiving antenna is the result of summing the electromagnetic fields obtained by each point (element) of the receiving aperture. In this case, each of the components is the result of the addition of the fields of all points of the transmitting aperture taking into account the amplitudes and phases obtained as a result by summation of «direct» and reflected from the earth's surface waves. As a result, a complex amplitude-phase structure of the field is usually formed in the plane of the receiving antenna. In this case, an important role is played by the correct choice of geometric dimensions of the receiving antenna aperture, especially in the vertical plane.
The representation of the receiving antenna as a spatially distributed structure allows to take into account the complex amplitude-phase structure of the electromagnetic field in the aperture of the receiving antenna and to assess the effect of its vertical size on the relative level of the received signal. The dependence of the relative signal level on the vertical size of the antenna has the form of a monotonically increasing function, while the dependence of the signal deviation from this size is periodic in nature with pronounced highs and lows. In this regard, it is possible to optimize the vertical size of the antenna in order to achieve the maximum level of the received signal with minimal impact of changes in the height of the antenna center due to inaccuracy of the antenna installation.
The proposed mathematical model allows us to take into account the complex structure of the electromagnetic field at the earth's surface, to determine the optimal spatial location of the antennas. The results of a model study of the ground radio line of communication in the centimeter wave range showed a significant impact of the vertical size of the antennas used on the characteristics of the ground radio line of communication and the ability to optimize these characteristics by the maximum of the received signal with minimal influence of inaccuracy installation of the antenna.
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