volume | PIER Journals

2020-06-10

The Upper Bound of the Speed of Propagation of Waves Along a Transmission Line

Vernon Cooray,

Professor Vernon Cooray

Division for Electricity

Uppsala University

Sweden

Homepage

Gerald Cooray,

Dr. Gerald Cooray

Karolinska Inst

Sweden

Homepage

Farhad Rachidi,

Dr. Farhad Rachidi

Swiss Federal Institute of Technology Lausanne

Switzerland

Homepage

Marcos Rubinstein

Dr. Marcos Rubinstein

Institute for Information and Communication Technologies, HEIG-VD

Switzerland

Homepage

Progress In Electromagnetics Research M, Vol. 93, 119-125, 2020

doi:10.2528/PIERM20040304

Abstract

According to theory, once certain conditions are fulfilled, current and voltage pulses propagate along ideal transmission lines with the speed of light. One can reach such a conclusion only when the conductors are assumed to be perfectly conducting, which cannot be realized in practice. A wave can only propagate along a transmission line with the speed of light if no energy has to be spent in establishing the current in the conductor. However, in establishing a current in a transmission line, energy has to be supplied to the electrons to set them in motion since they have a mass. The energy transfer to the electrons manifests itself in the form of an inductance which is called the kinetic inductance. The effect of the kinetic inductance has to be taken into account in signal propagation along high carrier mobility conductors including super conductors. In the case of transmission lines, the kinetic inductance leads to a change in the characteristic impedance and a reduction in the speed of propagation of waves along the transmission line. The goal of this paper is to show that the kinetic inductance will set an upper bound to the speed of propagation of waves along transmission lines, which is smaller than the speed of light.

Citation

Copy Export

Vernon Cooray, Gerald Cooray, Farhad Rachidi, and Marcos Rubinstein, "The Upper Bound of the Speed of Propagation of Waves Along a Transmission Line," Progress In Electromagnetics Research M, Vol. 93, 119-125, 2020.
doi:10.2528/PIERM20040304

References

1. Magnusson, P. C., G. C. Alexander, and V. K. Tripathi, Transmission Lines and Wave Propagation, CRC Press, London, 1992.

2. Collier, R. J., Transmission Lines: Equivalent Circuits, Electromagnetic Theory, and Photons, Cambridge University Press, UK, 2014.

3. Schelkunoff, S. A., "The electromagnetic theory of coaxial transmission lines and cylindrical shields," Bell Syst. Tech. J., Vol. 13, 532-578, 1934.
doi:10.1002/j.1538-7305.1934.tb00679.x

4. Nucci, C. A., F. Rachidi, and M. Rubinstein, "Interaction of electromagnetic fields with overhead and underground cables," Lightning Electromagnetics, V. Cooray (ed.), IET publishers, London, 2012.

5. Ramo, S., T. V. Duzer, and J. R. Whinnery, Fields and Waves in Communication Electronics, Wiley, 2008.

6. Boras, V., S. Vujevic, and D. Lovric, "Definition and computation of cylindrical conductor internal impedance for large parameters," 2010 Conference Proceedings ICECom, 20th International Conference on Applied Electromagnetics and Communications, 2010.

7. Jackson, J. D., Classical Electrodynamics, John Wiely & Sons, New York, 1975.

8., University of Oxford, webpage, Communications engineering, Research, Ultrafast electronics, 2016 (http://www.eng.ox.ac.uk/communications/research/ultrafast-electronics/ultrafast-researchprojects/kinetic-inductance).

9. Annunziata, A. J., et al. "Tuneable superconducting nano-inductors," Nanotechnology, Vol. 21, No. 44, 445202, 2010.
doi:10.1088/0957-4484/21/44/445202

10. Cholachue, C., B. Ravelo, A. Simoens, A. Fathallah, M. Veronneau, and O. Maurice, "Braid shielding effectiveness Kron’s Model via coupled cables configuration," IEEE Transactions on Circuits and Systems II: Express Briefs, 1-5, Early Access, 2019.

11. Ravelo, B. and O. Maurice, "Kron-Branin Modeling of Y-Y-Tree interconnects for the PCB signal integrity analysis," IEEE Transactions on Electromagnetic Compatibility, Vol. 59, No. 2, 411-419, Apr. 2017.
doi:10.1109/TEMC.2016.2610519