On Jun 25, 5:25*pm, John S wrote:
But, it does. First, it causes the 50 ohms line (looking into the 291.4
ohms line to see a match due to the reflection. Second, the
re-reflection from that discontinuity is half of what maintains the
circulating energy on the line. The other half is the discontinuity of
the non-virtual load.

You are confusing reflection with wave cancellation (destructive
interference). I suggest that you study the separate sections on
reflections vs interference in "Optics", by Hecht. Nowhere does any
optical textbook indicate that superposition and reflection are the
same thing (and they are indeed NOT the same thing).

Superposition/interference applies to two or more waves. Reflection
applies to a single wave. When a reflected wave is re-reflected, it is
always a single wave event. Take a look at one of the s-parameter
equations:

b1 = s11(a1) + s12(a2) = 0

b1 is the reflected voltage toward the source which is, of course,
zero when looking into a Z0-match.

s11(a1) is the forward source wave reflected from the physical
impedance discontinuity at the Z0-match point. Note: This is a single
reflected component of a single forward wave.

s12(a2) is the part of the reflected wave from the load that is
transmitted back through the impedance discontinuity at the Z0-match
point. Note: This is a single transmitted component of a single
reflected wave.

Reflections are now over and done with. What happens next is
superposition/interference, i.e. the phasor addition of the two
component reflections. Note: The results of the phasor addition of two
component waves is NOT a reflection!!!

The zero result of the addition of those two phasors is associated
with destructive interference toward the load. That's what causes the
50 ohm Z0-match, not the component reflections. The redistribution of
the destructive interference energy back toward the load is NOT a re-
reflection and here's why:

A re-reflection preserves the modulation content of the re-reflected
wave which can be proved by TV ghosting experiments. Wave cancellation
due to destructive interference does NOT preserve the modulation. In
fact, any differences in modulation between the two superposed wave
components would wind up incident upon the source.
--
73, Cecil, w5dxp.com