Reg Edwards wrote:

Given a line's primary characteristics, R,L,C,G,
length, or it's secondary characteristics Zo, dB, phase
angle, plus the line's terminatiing impedance it is
possible to calculate, by classical methods, all other
quantities of engineering interest - WITHOUT ANY
REFERENCE TO REFLECTION COEFFICIENT OR SWR which are
mere man-made notions supposed to assist understanding
of what goes on in the real world but, as exchanges on
this newsgroup show, are just a pair of bloody useless
nuisances.

Nevertheless, the outer circle of the Smith chart
is *always*
the locus of zero positive resistance and infinite
SWR, and a rho vector cannot terminate on, or
cross over, this circle when a load R0 is
present, regardless of the rest of the circuit,
including any possible combination of resistances
and reactances and complex Z0.

One can argue "ignore rho=1 and just jump over
it". This cannot be done in good mathematics.

Dismissing rho and SWR as "contrived nuisances" is
a convenient way to get rid of this problem, but
it does not "wash". Rho and SWR are fundamental
properties of transmission lines that do not go
away, and a non-zero R precludes rho=1.0.

Any attempt to circumvent (bypass) these small
inconveniences is doomed to failure, regardless of
the analytic geometry considerations.

Bill W0IYH