I've mentioned a couple of times that I did an analysis of a fictitious
lossless line with complex Z0, noting that such a line couldn't be
constructed. This academic exercise was done by duplicating the
lossy-line analysis, but with loss constant alpha set to zero. With a
one wavelength line, all the results were consistent. However, after
looking more carefully at the lossless line analysis, I've found that
the law of conservation of energy is violated except for certain line
lengths. That is, the total average power into the "lossless" line isn't
always equal to the average power out. (The one wavelength I chose for
the analysis turned out to be one of the special cases where the average
power in does equal the average power out.) Of course, loss constant
alpha and line impedance Z0 aren't actually independent; both are
derived from the same R, C, L, and G parameters. Although I knew this, I
didn't realize what the consequence would be of assigning an impossible
combination of values to Z0 and alpha. The consequence turns out to be
that voltages, currents, and impedances are all consistent, but total
average power is not. I haven't posted the lossless line analysis, and
won't, since the results are invalid because of the invalid premises. I
believe that any valid analysis must use loss constant alpha,
propagation constant beta, and characteristic impedance Z0 which are all
derived from the same R, C, L, and G parameters -- as was the case for
the lossy-line analysis I posted.

I continue to believe and assert that the lossy-line analysis I did post
is valid for any line length, and haven't seen any evidence to the contrary.

Roy Lewallen, W7EL