Potentials of the Application of the Electrical Transmission Line Theory for Thermal Investigations on Cables

In this contribution, similarities and differences between electrical and thermal effects on cables are investigated. In the electrical transmission line theory, a wide variety of methods is known to describe the voltage and current along cables. The potential for the adaption of some of those methods to thermal problems is discussed. Exemplarily, for an unshielded single cable, an analytical solution based on the Laplace transform and an approach based on cascaded equivalent circuits are compared with a numerical reference solution and measurement results.

Analogue Hawking Radiation in Nonlinear LC Transmission Lines

Analogue systems are used to test Hawking radiation, which is hard to observe in actual black holes. One such system is the electrical transmission line, but it suffers the inevitable issue of excess heat that collapses the successfully generated analogue black holes. Soliton provides a possible solution to this problem due to its stable propagation without unnecessary energy dissipation in nonlinear transmission lines. In this work, we propose analogue Hawking radiation in a nonlinear LC transmission line including nonlinear capacitors with a third-order nonlinearity in voltage. We show that this line supports voltage soliton that obeys the nonlinear Schrödinger equation by using the discrete reductive perturbation method. The voltage soliton spatially modifies the velocity of the electromagnetic wave through the Kerr effect, resulting in an event horizon where the velocity of the electromagnetic wave is equal to the soliton velocity. Therefore, Hawking radiation bears soliton characteristics, which significantly contribute to distinguishing it from other radiation.