Open AccessRelativistic Doppler effect in an extending transmission line: Application to lightning
Author(s) -
Shoory Abdolhamid,
Rachidi Farhad,
Rubinstein Marcos
Publication year - 2011
Publication title -
journal of geophysical research: atmospheres
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.67
H-Index - 298
eISSN - 2156-2202
pISSN - 0148-0227
DOI - 10.1029/2010jd015279
Subject(s) - physics , doppler effect , transmission line , computational physics , reflection (computer programming) , distortion (music) , optics , reflection coefficient , line (geometry) , lorentz transformation , wave propagation , acoustics , classical mechanics , computer science , mathematics , telecommunications , geometry , amplifier , optoelectronics , cmos , astronomy , programming language
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.