AI4QJ wrote:
"Richard Clark" wrote in message
...
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..._Impedance.pdf
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.

So far as we know, the maximum velocity permitted in the universe is the
speed of light, which is the speed of electromagnetic disturbance. Here
we disturb the transmission line electromagnetically. Think of the
velocity of the wave front as a moving wall. Everything behind the
moving wall is charged to the applied voltage, everything in front is
uncharged. The ratio of voltage to current turns out to be a pure
resistance, dependent only on the capacity per length and wave velocity.

Before becoming too critical or skeptical, run the equation with the
characteristics from a few transmission lines. You will find that the
numbers are very close, but not exact. The published characteristics
are not carried out to many decimal places, and who knows to what
accuracy they were determined.

73, Roger, W7WKB