23-30

UDC 621.37
DOI: 10.15350/2306-2819.2018.4.23

VOLTAGE IN A NONUNIFORM DATA TRANSMISSION LINE

O. Sh. Dautov¹, L. Yu. Fadeeva¹, V. P. Ivanov²
¹Kazan National Research Technical University named after A. N. Tupolev (KNRTU-KAI),
10, K. Marx Street, Kazan, 420111, Russian Federation
E-mail: dautov_kstu@mail.ru
²State Institute of Applied Optics,
2, Lipatov St., Kazan, 420075, Russian Federation

ABSTRACT

Introduction. The determination of voltage in a nonuniform data transmission line is of great interest to numerous applications. There are two approaches to its solution. The matrix approach is applied for a piecewise-homogenous transmission line. It allows determining values of secondary parameters of the circuit, voltage and the current in each line segment sequentially and it also requires matrix multiplication. The number of matrices usually corresponds to the number of heterogeneities, included in the transmission line. It leads to fast error accumulation. Therefore, the matrix approach is acceptable only if heterogeneities are occasional. The second method is based on the solution of the differential equation. At present it seems to be a fact that there is no general method of the solution of the linear differential equation higher than the first order. The purpose of the work is the development of the method of calculations of voltage and currents in the nonuniform transmission line, free of matrix approach limitations. Interpretation of results and their analysis. In order to interpret the physical content of the obtained solution, the example of the analysis of the steady regime of sinusoidal voltage in the transmission line with variable line parameters was considered. Conclusion. The representation of the total voltage in the nonuniform line, occurring with the single power supply with the passive load at the opposite end was obtained.

KEYWORDS

differential equation; primary line parameters; voltage; inhomogeneous line

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For citation: Dautov O. Sh., Fadeeva L. Yu., Ivanov V. P. Voltage in a Nonuniform Data Transmission Line. Vestnik of Volga State University of Technology. Ser.: Radio Engineering and Infocommunication Systems. 2018. No 4 (40). Pp. 23-30. DOI: 10.15350/2306-2819.2018.4.23