File:Telegrapher equation.gif
Telegrapher_equation.gif (360 × 256 pixels, file size: 686 KB, MIME type: image/gif, looped, 101 frames)
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Summary[edit]
DescriptionTelegrapher equation.gif |
English: The telegrapher's equation describes a signal propagation in a transmission line. If the wires have no resistance and the dielectric separating them is a perfect insulator, it reduces to the wave equation. Otherwise both dispersion and losses are present.
Italiano: L'equazione del telegrafista descrive la propagazione di un segnale in una linea di trasmissione. Se i cavi hanno resistenza zero e il dielettrico che li separa è un isolante perfetto questa si riduce alla semplice equazione delle onde. Altrimenti la soluzione è dispersiva (frequenze diverse si muovono a velocità diverse) ed è presente assorbimento. |
Date | |
Source | https://twitter.com/j_bertolotti/status/1172517281374572551 |
Author | Jacopo Bertolotti |
Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code[edit]
(*Find the dispersion relation for the Telegrapher's equation*) f = E^(I (k x - \[Omega] t)); FullSimplify[D[f, {t, 2}] - v^2 D[f, {x, 2}] + b D[f, t] + c f] Solve[c + k^2 v^2 + (-I b - \[Omega]) \[Omega] == 0, \[Omega]] (*Plot a pulse both with and without dispersion*) g = Sum[(E^(I k x) E^(-(k - k0)^2/(2 \[Sigma]^2)) E^(-I \[Omega] t)) /. {\[Omega] -> 1/2 (-I b + Abs[Sqrt[-b^2 + 4 c + 4 k^2 v^2]])} /. {\[Sigma] ->1, k0 -> 4, b -> 0, c -> 0, v -> 1, t -> 15}, {k, 0, 15, 0.1}]; Show[ Plot[Re[g], {x, -10, 20}, PlotRange -> All, PlotStyle -> {Orange, Thick}] , Plot[{Abs[g], -Abs[g]}, {x, -10, 20}, PlotRange -> All, PlotStyle -> {Black, Black}] ]
Licensing[edit]
This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. | |
The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
http://creativecommons.org/publicdomain/zero/1.0/deed.enCC0Creative Commons Zero, Public Domain Dedicationfalsefalse |
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