The missing elements in the telegraph equations

Abstract

The conventional modeling of transmission lines relies on the classical telegraph equations, originally formulated over 150 years ago. These equations are typically derived by representing the line as an assembly of infinitesimal inductive, capacitive, and resistive elements. However, this formulation is fundamentally flawed, as a transmission line cannot be accurately described through a discretized model of infinitesimal lumped components. Instead, a more rigorous approach should derive the governing equations directly from Maxwells equations in conjunction with Ohms law. This paper presents such a derivation and introduces a corrected formulation, herein referred to as the Trump Equations.