Equivalent random propagation time for coaxial cables

TL;DR

This paper demonstrates that the propagation time in coaxial cables can be modeled as a stable random variable, similar to acoustic propagation, providing a new probabilistic perspective on signal transmission in cables.

Contribution

It extends the stable distribution model of propagation time from acoustic waves to electromagnetic signals in coaxial cables, offering a novel analytical approach.

Findings

Propagation time in coaxial cables follows a stable distribution.

The model aligns with the exponential transfer function of cables.

Provides a probabilistic framework for analyzing cable signal propagation.

Abstract

Propagation of monochromatic electromagnetic waves in free space results in a widening of the spectral line. On the contrary, propagation preserves monochromaticity in the case of acoustic waves. In this case, the propagation can be modelled by a linear invariant filter leading to attenuations and phases changes. Due to the Beer-Lambert law, the associated transfer function is an exponential of power functions with frequency-dependent parameters. In recent papers, we have proved that the acoustic propagation time can be modelled as a random variable following a stable probability distribution. In this paper, we show that the same model can be applied to the propagation in coaxial cables.