Explicit formulas for currents at branching long lines and for maximum of current amplitudes

TL;DR

This paper derives explicit formulas for currents and voltages in networks of long lines using telegrapher's equations, facilitating analysis of maximum current amplitudes and network robustness to external influences.

Contribution

It provides explicit formulas for Fourier transforms of currents and voltages in long line networks, enabling analytical and computational studies of network behavior.

Findings

Formulas for maximum current amplitudes derived

Enhanced understanding of network robustness to impulses

Operational solution approach applied to graph-based PDEs

Abstract

A system of 'telegrapher's' equations for a number of long lines joined into a network is studied. Explicit formulas for Fourier transforms of current and voltage are derived. These formulas are very suitable for computer application as well as for the analytical study of processes o networks. As an example, the availability of formulas aids the derivation of explicit formulas for maxima of current amplitude over the given class of admissible external influences. These values may be used to indicate the characteristic of network robustness to excess voltage or electromagnetic impulse. The approach is based on the operational solution already proposed by the author for more general partial differential equations on graphs.