Keith Dysart wrote:
On Jan 1, 1:20 pm, Roger wrote:
Discussing forward and reflecting waves, when is stability reached.





Roy Lewallen wrote:
If "stability" means steady state, a transmission line with any
resistance at either end or both ends is less complicated to analyze
than the particularly difficult lossless case I used for my analysis
which never reaches a true steady state. The presence of resistance
allows the system to settle to steady state, and that process can easily
and quantifiably be shown. And in two special cases, the process from
turn-on to steady state is trivially simple -- If the line is terminated
with Z0 (technically, its conjugate, but the two are the same for a
lossless line since Z0 is purely resistive), steady state is reached
just as soon as the initial forward wave arrives at the far end of the
line. No reflections at all are present or needed for the analysis. The
second simple case is when the source impedance equals Z0, resulting in
a source reflection coefficient of zero. In that case, there is a single
reflection from the far end (assuming it's not also terminated with Z0),
but no re-reflection from the source, and steady state is reached as
soon as the first reflected wave arrives at the source.
Roy Lewallen, W7EL
Could you better describe how you determine that the source has a Z0
equal to the line Z0? I can guess that you use a Thévenin equivalent
circuit and set the series resistor to Z0.

This will do it. As will a Norton with the parallel
resistor set to Z0.

The power output of the Thévenin equivalent circuit follows the load.
Therefore, when the load delivers power, the Thévenin equivalent circuit
adsorbs power. Right?

This apparently simple question has a very complicated
answer that depends on what precisely is meant by
"load delivers power" and "circuit absorbs power".

If by "load delivers power", you mean the reflected
wave, then this may or may not (depending on the
phase), mean that energy is transfered into the
generator.

If you mean that the time averaged product of
the actual voltage and current at the generator
terminals show a transfer of energy into the
generator, then energy is indeed flowing into
the generator.

If by "circuit absorbs power", you mean that
there is an increase in the energy dissipated
in the generator, this can not be ascertained
without detailed knowledge of the internal
arrangement of the generator and also depends
the meaning of "load delivers power", discussed
above.

...Keith

I think we will find it simpler than that.

I posted some links to descriptions of ideal voltage sources. After
reading them, I am taking another look at how we define impedance from
an ideal voltage source in a separate posting. You may wish to read the
links, and hopefully, my posting.

Here are the links:

Voltage source:
http://en.wikipedia.org/wiki/Voltage_source

Thévenin equivalent circuit:
http://en.wikipedia.org/wiki/Th%C3%A9venin%27s_theorem

73, Roger, W7WKB