A mathematical model for electromagnetic oscillation propagation that accounts for single and dual-phase lag

Abstract

Telegrapher’s equations that account for the speed and acceleration of a current and voltage were derived using a modified Ohm’s law formula that includes relaxation components. Examining the exact analytical solutions to these equations allowed us to conclude that abrupt changes in the target functions observed in solutions to classic telegrapher’s equations were eliminated, which indicates the elimination of the infinite propagation speed of electric field potentials inherent in the classic Ohm’s law formula. Analysis of the analytical solutions showed the impossibility of instant current (voltage) adoption at the edges of the conductor at the initial time instant, as the process of establishing these edges requires a definite initial time interval. This serves as evidence that it is physically impossible to instantly set a boundary condition in an actual electric conductivity process.

KEYWORDS:

• Telegrapher’s equation
• DPL model
• relaxation properties of a medium
• exact analytical solution
• modified Ohm’s law
• relaxation factors
• electric lines
• equally distributed parameters

Acknowledgments

The reported study was funded by RFBR, project number 20-38-70021.

In accordance with Taylor & Francis policy and our ethical obligation as a researcher, we are reporting that there are no conflicts of interest to declare.

Disclosure statement

No potential conflict of interest was reported by the authors.