학술논문

Phase Space Analysis of the Telegraph Equation
Document Type
Periodical
Source
IEEE Transactions on Antennas and Propagation IEEE Trans. Antennas Propagat. Antennas and Propagation, IEEE Transactions on. 70(10):9687-9693 Oct, 2022
Subject
Fields, Waves and Electromagnetics
Aerospace
Transportation
Components, Circuits, Devices and Systems
Dispersion
Time-frequency analysis
Transmission line theory
Phase distortion
Damping
Power cables
Green's function methods
phase space
wave propagation
Wigner distribution
Language
ISSN
0018-926X
1558-2221
Abstract
We present a new approach to the study of the telegraph equation, which is based on analyzing the equation in phase space. We consider the phase space of time and frequency, as well as of position and spatial frequency (or wavenumber). We show that considerable simplification, both conceptual and mathematical, results from this approach. The basic reason why a phase space approach is fruitful is that when there is dispersion, the group velocity is not constant but changes with frequency, and therefore the wave changes as it propagates over space and time. Simple but effective and insightful phase space approximations to the solution of the telegraph equation are presented, with examples.