Jim Kelley wrote:
Redistribution is an interaction....interesting. But, you were
telling us about how waves interact with other waves. I'm interested
to know what effect x has on y, and vice versa? We have x + y making
z. So after that, tell us how have x and y changed as a result of
their "interaction"?

In a transmision line, when z=0, x and y are permanently
changed. Their energy components combine into one re-reflected
wave. The separate identities of x and y disappear at the
instant that z becomes zero.

In order to measure s11 and s12, a2 is turned off. The result is:

a1----|
|----s21(a2)
s11(a1)----|

Note that s11(a1) has already reflected from the impedance
discontinuity and there are no other impedance discontinuities
between it and the source. Should be smooth sailing.

In order to measure s21 and s22, a1 is turned off. The result is:

|----s22(a2)
s12(a2)----|
|----a2

Note that s12(a2) has already passed through the impedance
discontinuity and there are no other impedance discontinuities
between it and the source. Should be smooth sailing.

s11(a1) and s12(a2) are your two waves. They exist and are
so measurable that their measurements results in knowing
the value of s11 and s12.

For b1 = s11(a1) + s12(a2) = 0, s11(a1) and s12(a2) must
be of equal magnitude and opposite phase. That's exactly
what happens at a Z0-match.

s11(a1) and s12(a2) *never* encounter an impedance discontinuity.
They are effects of a1 and a2 encountering an impedance discontinuity.
The only thing s11(a1) and s12(a2) encounter are each other and that
interaction completely changes those two waves. The two waves cancel
and their energy components are re-distributed in the opposite
direction. s11(a1) and s12(a2) never encounter an impedance
discontinuity.
--
73, Cecil http://www.w5dxp.com