Relativistic Doppler effect in an extending transmission line : application to lightning

Shoory, Abdolhamid (EPFL,Lausanne, Switzerland) ; Rachidi, Farhad (EPFL, Lausanne, Switzerland) ; Rubinstein, Marcos (School of Management and Engineering Vaud, HES-SO // University of Applied Sciences Western Switzerland)

We present in this paper a thorough analysis of current wave propagation with arbitrary speed along an extending transmission line. We derive rigorous analytical equations in the time and frequency domains expressing the reflections of the current wave occurring at the extending end of the line. The derived equations reveal that it is not possible to represent current reflections occurring at the extending end of a transmission line using a constant, frequency‐independent reflection coefficient, as previously done in the literature. The reflected wave from the extending end of the line is shown to be affected by the Doppler frequency shift. In other words, the reflected wave from an extending transmission line suffers distortion, the amount of which depends on the incident wave form, its frequency content, and the speed of the extending end of the line. The derived expression is in agreement with the relativistic Doppler effect and is consistent with the Lorentz transformation. Finally, engineering models for return strokes are generalized and closed‐form analytical expressions are derived for the spatial‐temporal distribution of the current along the channel accounting for reflections at ground and at the return stroke wave front taking into account the Doppler effect.


Article Type:
scientifique
Faculty:
Ingénierie et Architecture
School:
HEIG-VD
Institute:
IICT - Institut des Technologies de l'Information et de la Communication
Date:
2011-07
Pagination:
8 p.
Published in:
Journal of Geophysical Research
Numeration (vol. no.):
2011, vol. 116, no. D13
DOI:
ISSN:
0148-0227
Appears in Collection:



 Record created 2020-07-07, last modified 2020-07-09

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