"AI4QJ" wrote in message
...

"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)

actually it is what you are looking for, you have just, again,
misinterpreted the results. in the DC case you have to remember that not
only is f=0, but wavelenght is infinite. so a shorted stub of any length of
transmission line appears to be 0% of a wavelength. using the normal
equations, or smith chart, to transform the impedance at the far end of the
line to the connection point will result in exactly the same impedance at
the connection point as is at the far end. so feed a DC current into a
shorted line of any length and in steady state you get infinite
current(assuming no loss in the line of course), use an open line and you
get zero current. put a resistive load out there and you see the load
resistance. it all works, you just have to know what to look for and just
what the conditions you have specified really mean.

as far as probing the 'black box' with varying frequencies or pulses to see
what is in it, you again must more clearly state the conditions. when it
was suggested that you could stick all the different circuits you used to
obtain the same impedance in a box and it was added to that a single
capacitor would look the same, the implicit assumption is that you are ONLY
going to examine the circuits in sinusoidal steady state at a single
frequency. that is the ONLY case where that type of replacement is valid.
if you allow transients or multiple frequencies than you can not substitute
a 'black box' for the unknown circuit. refer to any book from a circuits
101 course for the full analysis.