AI4QJ wrote:
"Roger" wrote in message
. ..
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.

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

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

It was already stated that we should ignore the wavefront of the step
function. What we are left with is steady state. So impedance is not what
'we' are looking for.

(I sure am learning a lot about antennas and transmission lines here)


Yes, I am learning a lot also.

Well, I did not say we should ignore the wave front, just the opposite.
The wave front gives us the time marker so that velocity has meaning
in relationship to a length of transmission line.

Roy is giving good advice to study time domain reflectometry. One
reference I looked at used different pulse widths to examine for faults
at different distances. That makes sense to me.

Where did you get the formula for Zo that resulted in a zero impedance?

73, Roger, W7WKB