This general discussion sounds a lot like a description of a traditional
TDR system using a step function. You should be able to find quite a bit
of information about this process on the web.

A number of relationships among delay, Z0, velocity factor, and L and C
per unit length are quite useful, and I've used them for many years. For
example, a transmission line which is short in terms of wavelength at
the highest frequency of interest (related to the rise time when dealing
with step functions) can often be modeled with reasonable accuracy as a
lumped L or pi network. The values of the lumped components can easily
be calculated from the equations relating delay, Z0, L per unit length,
and C per unit length.

Strictly speaking, DC describes only the condition when a steady value
has existed for an infinite length of time. But a frequency spectrum of
finite width also requires a signal which has been unchanging (except
for periodic variation) for an infinite time. In both cases, we can
approximate the condition with adequate accuracy without having to wait
an infinite length of time. In the case of a step response, we wait
until all the aberrations have settled, after which the response is for
practical purposes the DC response. People used to frequency domain
analysis having trouble with the concept of DC characteristics and
responses can often get around the difficulty by looking at DC as a
limiting case of low frequency.

I don't know if it's relevant to the discussion, but the velocity factor
of many transmission lines is a function of frequency. A classic example
is microstrip line, which exhibits this dispersive property because the
fractions of field in the air and dielectric changes with frequency.
Coaxial line, however, isn't dispersive (assuming that the dielectric
constant of the insulator doesn't change with frequency) because the
field is entirely in the dielectric. It will, therefore, exhibit a
constant velocity factor down to an arbitrarily low frequency -- to DC,
you might say. Waveguides, however, are generally dispersive for other
reasons despite the air dielectric. The shape of the step response of a
dispersive line is very distinctive, and is easily recognized by someone
accustomed to doing time domain analysis.

There seems to be a constant search on this newsgroup for amazing new
principles, and "discoveries" are constantly being made by
misinterpretation and partial understanding of very well established
principles. I sense that happening here. Anyone who's really interested
in gaining a deeper understanding of transmission line principles and
operation can benefit from a bit of study of time domain reflectometry
and other time domain applications. All the fundamental rules are
exactly the same, but the practical manifestations are different enough
that it can give you a whole new level of understanding.

Roy Lewallen, W7EL