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.

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

73, Roger, W7WKB