On Sun, 30 Dec 2007 19:08:44 -0800, Roger wrote:

No, my concept of transmission lines deals fine with linear sources, it
is the non-linear constant voltage source and constant current source
that can not handle a second source of power arriving at a time later
than the original pulse.

Hi Roger,

That is not the problem of the sources, it is your problem alone in
coming to terms with the network. Any reference that reaches deep
into the fundamentals of lines and networks begins with the Thevenin
source (and at least one off of my shelf delves into two Thevenin
sources facing each other).
"There are waves of identical frequency traveling
in both directions on the line, but their amplitudes
and phases are independently variable,
and neither can be called "incident" or "reflected"
waves."

It is notable that the author expressly offers only one set of
equations for the distributed voltage and current along a line and
distinctly says:
"It is worth noting that (8.1) and (8.2) [those equations]
are also applicable to Fig. 8-2 below [showing the dual
source configuration with deliberate matches], a
distinctly different transmission line circuit."

What makes it "a distinctly different transmission line circuit" is
that it is in fact one source feeding both ends. It settles the hash
about frequency, phase, coherence, amplitude, matching, and all the
other folderol that attends many of Cecil's jejune postings:
"Here a single source supplies signals to both ends
of a transmission line section, through networks that terminate
the section in its characteristic impedance at each end."

As time
passes, I will try to improve the concept of the perfect POWER source to
see if that can bridge the conceptual differences, but retain the
relative simplicity of sine waves adding.

The two equations, needing no reference to a constant power source:
V(z) = V1· e^-y·z + V2· e^+y·z
I(z) = (V1· e^-y·z - V2· e^+y·z) / Zo
where
z: the distance along a line
y = a + jB
a: nepers per unit length of line
B = 2 · pi / wavelength
V1 & V2 are arbitrary voltage phasors to be determined by
boundary conditions at the ends of the line.

It took very little effort to then proceed to the obvious:
"Whenever two waves of identical frequency travel
in opposite directions on a transmission line ...
the fundamental phenomenon of interference or
'standing waves' occurs. ... exhibits periodic maxima
and minima ... in its most striking form when
the two oppositely directed waves have equal
amplitude and the transmission line system has
zero attenuation."

Elaborations of stepped pulses of energy had better resolve to
identical analysis using the math above, or the strain of elaboration
has led to sterile inventions.

73's
Richard Clark, KB7QHC