A coax is only applicable for frequencies where
the TEM mode is the only possible mode, that is
below the cut-off frequencies of higher order TM
and TE modes. For these frequencies the n and thus
the phase velocity v_p are pretty constant, and
the group velocity v_g = v_p.
(If they weren't equal, the coax would be dispersive
and unusable.)
If you write the phase(t,x) = (wt - kx)
then v_p = w/k and v_g = dw/dk
If w = v_p.k is linear, that is v_p constant with respect to k,
then v_g = dw/dk = w/k = v_p
So when we are talking about coax cables, 'propagation speed',
'phase velocity', 'group velocity' and 'signal speed' are all
the same speed, and this speed depends only on the refraction
index of the dielectric, and is independent of the geometry
(the ratio D/d).
So yes, you did object to my reasoning about the phase speed
in a coax, and yes, this was the speed Sylvia measured.
>
> 1/ Signal phase speed, that has no c limit, as carries no information.
>
> 2/ Information propagation speed,
> e.g. the speed of a sent pulse or other signal
> to be detected, that has c limit.
Sure.
But this is irrelevant for our discussion about
the propagation speed in coax cables.
>
> E.g. in though experiment with a big enough no-dielectric coax,
> to neglect matter quantization effects
> ( You say geometry does not affect the speed )
> placed in ionosphere with used frequency near the resonance one,
> with n < 1,
>
> the phase speed is > c , while the info speed is not
A coax with filled with a plasma?
This doesn't make much sense to me, and I
won't bother to speculate how it would behave.
The ionosphere is a very complicated medium.
It is a plasma in a magnetic field. It is
highly dispersive and anisotropic.
So much so that a short pulse may be stretched
out to a long sinus wave with changing frequencies
which follows the magnetic field of the Earth.
"Whistler waves".
https://soundcloud.com/nasa/whistler-waves2
For GPS signals the most prominent effect of
the ionosphere is a delay (caused by v_g < c).
Fortunately, the ionosphere isn't so thick that
the dispersion will spoil the signal.
>
> So n cannot be the only factor affecting
> the info propagation speed along a coax,
> but probably the group speed as well.
Yes, n is the only factor affecting the info propagation
speed along a properly designed coax for the frequencies
below the cut-off frequency of higher order modes.
(Properly designed means that the n of the dielectric
must be constant for the frequencies mentioned above.)
Quite.
But a pulse is so strongly attenuated and
the dispersion is probably very high, so it
can't be used for information transmission.
>
> ( I admit I am not a signal theory expert,
> so I know about the group speed
> about what is written in its wikipedia article.)
>
--
Paul
https://paulba.no/