William E. Sabin wrote:

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


Power wave theory avoids the Smith chart, since
there are no transmission lines. Scattering
matrices are used instead. Nevertheless, rho is
still an important parameter, but it does not
involve distance separation between generator and
load as a parameter.

Bill W0IYH