On Dec 14, 7:59 pm, "AI4QJ" wrote:
"Roger" wrote in message

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AI4QJ wrote:
"Richard Clark" wrote in message
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In a 231 line posting that contains only original 57 lines:
On Thu, 13 Dec 2007 17:26:17 -0800, Roger wrote:

Hi Roger,

This last round has piqued my interest when we dipped into DC. Those
"formulas" would lead us to a DC wave velocity?
Hi Richard,

Here are two links to pages that cover the derivation of the formula
Zo
= 1/cC and much more.

http://www.speedingedge.com/PDF-File...stic_Impedance...
http://www.ece.uci.edu/docs/hspice/h...001_2-269.html

Here is the way I proposed to Kevin Schmidt nearly seven years ago
after
seeing him use the formula on a web page:
Hi Roger,

However, none of what you respond with actually gives a DC wave
velocity. At a stretch, it is a transient with the potential of an
infinite number of waves (which could suffer dispersion from the
line's frequency characteristics making for an infinite number of
velocities). The infinite is a trivial observation in the scheme of
things when we return to DC.

Attaching a battery casts it into a role of AC generation (for however
long the transmission line takes to settle to an irresolvable
ringing). Discarding the term DC returns us to conventional
transmission line mechanics.

DC, in and of itself, has no wave velocity.

For the model provided, R= 0, therefore we have a transmission line
consisting of superconductors. The speed at which steady state DC current
is injected into the model will equal the maximum speed of DC current in
the model. Although the electrons themselves will move very slowly, for
each coulomb injected in, one coulomb will be injected out at the same
velocity they were injected in (not to be confused with 'current' which
is the number of coulombs per second). If it were possible for the source
to provide DC current at c, then the DC current moves at c. The
capacitance C can be any value and Zo has no meaning. The only model that
works here is the one with a cardboard tube filled with ping pong balls,
in this case with 0 distance between them.

Ah, but of so little importance because the model is not reality.
While R (ohmic resistance) is specified as zero, impedance is what we are
looking for. Impedance is the ratio of voltage to current.

Roger the impedance is zero because the current is steady state DC. F = 0,

Zo = 0 -j*2*pi*0*C =0

I'd suggest that this is an inaccurate interpretation.
For an ideal line we have

Z0 = sqrt( L/C )
and
velocity = 1/sqrt( LC )

These are the fundamental equations based on the
charactistics (distributed L and C) of the line.

These equations can be manipulated to yield
Z0 = 1/(velocity * C)
and
Z0 = velocity * L

But Z0 continues to exist regardless of the signal
being applied.

Think of the "velocity" as the velocity at which a
perturbation to the signal propagates down the
line.

When you turn on the constant voltage, the step
propagates down the line at "velocity", when you
change the voltage, the new step propagates at
"velocity". Over any region of the line where
the signal has a constant amplitude, it will
be difficult to discern this "velocity" but on
other regions of the line where a change is
present, it will be possible.

So if there are no perturbations, the "velocity"
can not be observed, but it would a mistake
to think that it goes away (or that Z0 does).

....Keith