Signal transmission on lossy lines as a dissipative quantum state propagation

TL;DR

This paper models electric signal transmission on lossy coupled lines as dissipative quantum states, deriving exact solutions for wave propagation, velocity, and delay, and discusses measurement limitations and generalizations to complex networks.

Contribution

It introduces a novel calculation method for signal propagation on lossy lines, treating them as dissipative quantum states, and derives exact analytical expressions for key transmission parameters.

Findings

Exact Green function expressions for lossy line transmission

Derived formulas for information transfer velocity and time delay

Identified fundamental measurement accuracy restrictions

Abstract

The transmission of electric signals on a coupled line with distributed RLC-parameters is considered as a propagation of a dissipative quasi particle. A calculation technique is developed, alternative to the one, accepted for lumped lines. The relativistic wave equation for the transient response is deduced following the common Ohm-low-type considerations. The exact expressions for the Green function, for information transfer velocity and for time delay are obtained on this base. The fundamental restrictions on the measurement accuracy of the time delay are pointed out. The obtained results are naturally generalized for the multilevel networks of the arbitrary dimension.