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Summary
| Description |
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.
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| Date | |
| Source | https://twitter.com/j_bertolotti/status/1172517281374572551 |
| Author | Jacopo Bertolotti |
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Permission
( Reusing this file ) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
(*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
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication . |
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