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According to electric calculations, the overhead system and power lines being the part of the railway power supply are distributed parameters circuits. Wave processes in the overhead system have a negative impact on the power supply lines, laid in the vicinity of the railway, and increase the power losses in the traction power supply system. For the study of wave processes the method of mathematical modeling of non-sinusoidal signals transmission to the uniform two-wire distributed parameters line is provided. The mathematical model is based on the well-known line differential equations (telegraph equations) using Fourier series. The power line is a three-wire line. The paper presents an algorithm to bring the power line equations to the form of two-wire line equations. To assess the correctness of the mathematical model the research was carried out on the physical model of the line. Using the mathematical model there were given the findings of distributed parameters circuits various modes. The proposed method of mathematical modeling of different shape signals transmission to the distributed parameters line adequately reflects the phenomena occurring in the line and can be used for the analysis of electromagnetic processes both in the overhead system and power lines.

This paper examines the feasibility of locating rolling stock on a track section based on the track line's input impedance, taking into account the influence of its hardware parameters and external factors. The aim of the paper is to evaluate the feasibility of using the track section's complex input impedance to pinpoint rolling stock locations in conventional track circuits. The article presents the results of modeling changes in the track section's input impedance using a 25 Hz code track circuit, traditionally used on railways in the Russian Federation and the CIS. Three basic track circuit calculation modes were used as input data: normal, shunt, and control. Using the analytical expressions of classical track circuit theory for these modes and the Smath Studio software package, graphs were obtained of the active and reactive components of the complex input impedance versus insulation resistance, the ordinate of the rolling stock's location, and the location of the rail break. The simulation results demonstrated that it is possible to use the complex input impedance of a track section to determine the location of rolling stock with an accuracy of 50 meters and pinpoint the location of a rail break with an accuracy of 100 meters. These results can be used in the development of rolling stock tracking systems, including high-speed vehicles, as well as in diagnostic systems for rail network components, which will ultimately enable the transition to predictive failure detection systems.

Developed Methodology let make the calculation of coaxial cable parameters with account of the frequency of the transmitted signal. The comparative analysis of parameters of RC 50-7-28 and RG142 cables has been made with the values have been got by the measuring with the circuit analyzer according to the reference book with the results of the calculations. Check the accuracy of the calculation has pointed out the necessity for account of complementary factors for the purpose of much more correct account cable attenuation in the frequency spectrum.

The authors consider the question of the limits of applicability of the capacitor method for measuring the real part of the dielectric constant of printed circuit boards and telecommunications cabled rail transport using the example of FR-4 fiberglass laminate and the cable PK-75-4-12 in the frequency range from 10 Hz to 100 MHz. The measurements were carried out at a constant temperature and humidity of a known material. Comparison of the obtained values with the passport data on the material is carried out; a measurement procedure is developed with overlapping frequency ranges by changing the values of the measuring resistors from larger to smaller with increasing frequency of the input signal. It is shown that in the high-frequency region, the measurement accuracy is directly affected by the parasitic inductance of the capacitor sample under study, as well as the active resistance of the leads and plates and its increase due to the skin effect. The article also discusses the ways of accounting and calculating the parasitic elements of a capacitor. One of these ways is to study the characteristics of the elements of the sample at the first proper serial resonance of the capacitor under study.