Transients on lossy transmission lines with arbitrary boundary conditions

In this work the problem of transients on a lossy transmission line terminated by an arbitrary, including nonlinear, load is formulated. The tranmission line parameters are the constants R, L, G , and C . The exact relation between the input and output voltages and currents in the form of two couple...

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Bibliographic Details
Published in:I.R.E. transactions on antennas and propagation 1984-04, Vol.32 (4), p.418-422
Main Authors: Mohammadian, A., Chen-To Tai
Format: Article
Language:English
Subjects:
Applied sciences
Boundary conditions
Circuit properties
Couplings
Electric, optical and optoelectronic circuits
Electronic circuits
Electronics
Exact sciences and technology
Integral equations
Kernel
Laplace equations
Miscellaneous
Power system transients
Propagation losses
Time domain analysis
Transmission lines
Voltage
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Summary:In this work the problem of transients on a lossy transmission line terminated by an arbitrary, including nonlinear, load is formulated. The tranmission line parameters are the constants R, L, G , and C . The exact relation between the input and output voltages and currents in the form of two coupled integral equations is derived by the Laplace transform method. It is shown that the kernels of the integral equations may be represented in terms of either Lommel functions or integrals involving zeroth order modified Bessel functions. Simultaneous (numerical) solutions of these integral equations fulfilling the boundary conditions at the input and output of the line yields the input and output voltages and currents on the line. Finally the exact analytical relations in time domain of the voltage and current at an arbitrary point on the line (and the voltages and currents at the input and output terminals) are derived. In all parts, the problem has been formulated in such a way as to impose the causality condition explicitly.
ISSN:0018-926X
0096-1973
1558-2221
DOI:10.1109/TAP.1984.1143328