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Publication# A new expression for the ground transient resistance matrix elements of multiconductor overhead transmission lines

Abstract

The ground impedance matrix elements of a multiconductor overhead transmission line do not have analytical inverse Fourier transforms in the time domain. Thus, in general, the ground transient resistance matrix elements are to be determined numerically. Using the low-frequency approximation analytical expressions are available for the ground transient resistance. These expressions present however a singularity at t = 0 and require a careful treatment in a direct time domain analysis. In this paper, we show that the singularity in the ground transient resistance is due to the low frequency approximation. Also, we show that at early times, the ground transient resistance elements tend to an asymptotic value, which depend on the line geometrical parameters and ground relative permittivity. Finally, we propose new expressions which are analytical, non-singular, and which describe, within the limits of transmission line theory, both the early-time and late-time behavior of ground transient resistance in a more accurate way. © 2002 Elsevier Science B.V. All rights reserved.

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In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency).

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A gyrator is a passive, linear, lossless, two-port electrical network element proposed in 1948 by Bernard D. H. Tellegen as a hypothetical fifth linear element after the resistor, capacitor, inductor and ideal transformer. Unlike the four conventional elements, the gyrator is non-reciprocal. Gyrators permit network realizations of two-(or-more)-port devices which cannot be realized with just the conventional four elements. In particular, gyrators make possible network realizations of isolators and circulators.

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In physics and mathematics, the Fourier transform (FT) is a transform that converts a function into a form that describes the frequencies present in the original function. The output of the transform is a complex-valued function of frequency. The term Fourier transform refers to both this complex-valued function and the mathematical operation. When a distinction needs to be made the Fourier transform is sometimes called the frequency domain representation of the original function.

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