Abstract
The article considers the physical processes associated with the propagation of electromagnetic oscillations in a long line, the size of which is the same or slightly greater than the length of the electromagnetic wave (not more than ten times). As a research method, the differential-symbolic method is used, which is applied to the modified equation of the telegraph line. The boundary conditions for the two-point problem as well as additional parameters that are coefficients for the first derivatives in terms of coordinate and time in comparison with the classical equation of the telegraph line are considered as parameters for controlling the process of propagation of electromagnetic oscillations. Based on the differential-symbolic method, the boundary conditions of the two-point problem are found, under which the most characteristic oscillatory processes are realized in a long line. Based on the research, it is possible to draw conclusions about the effectiveness of analytical methods for the analysis of specific technical objects and control of the processes that take place in them.
Highlights
The development of telecommunication technologies has led to an active search for new information transmission technologies which use complex chaotic signals [1], methods of signal processing [2] and modulation using artificial intelligence systems [3]
Computer simulation methods designed to calculate the characteristics of these devices and the precise selection of their parameters require accurate calculation of highfrequency processes occurring in signal circuits [10], and refined models of electromagnetic oscillation propagation can solve this problem
To model a homogeneous long line with external current and / or voltage sources, which we will hereinafter call an active long homogeneous line, we proposed a modified telegraph line equation in which the influence of external sources is modelled by adding the first derivatives in time and wave propagation coordinates
Summary
ФІЗИКА І ХІМІЯ ТВЕРДОГО ТІЛА Т. 22, No 1 (2021) С. 168-174 Фізико-математичні науки. R.L. The physical processes associated with the propagation of electromagnetic oscillations in a long line, the size of which is the same or slightly greater than the length of the electromagnetic wave (not more than ten times) are considered in the work. The differential-symbol method, which is applied to the modified equation of the telegraph line is used. The two-point conditions for the problem as well as additional parameters that are coefficients of the first derivatives in terms of coordinate and time in comparison with the classical equation of the telegraph line are considered as parameters for controlling the process of propagation of electromagnetic oscillations. Based on the differential-symbol method, the two-point in time conditions under which the most characteristic oscillatory processes are realized in a long line is found.
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