Cecil,

You completely ducked the question. How did those waves get there in the
first place? Hint: there are no laws for conservation of waves or
continuity of waves.

It is easy to set up a problem with physically unrealizable inputs. It
is pointless to try to solve such a problem, however.

We've been around this track a couple of times before. Neither of us has
changed.

Bye.

73,
Gene
W4SZ

Cecil Moore wrote:
Gene Fuller wrote:

Cecil,

Nice try.

You first.

Describe how you set up this coherent wave/anti-wave pair that happily
travel together for some indeterminate distance. Then I will describe
what happens when at some arbitrary point and time they decide to
annihilate.


Sure, here's the two coherent reflected waves that cancel at a
Z0-matched impedance discontinuity in a transmission line.

b1 = s11*a1 + s12*a2 = 0

I'm sure you recognize the S-parameter equation for the reflected
voltage flowing toward the source which is the phasor sum of two
other reflected voltages.

They don't travel together for some indeterminate distance. They
are cancelled within the first dl and dt. And they don't annihilate.
They simply cancel in the rearward direction.

Incidentally, if you square both sides of the equation you get

b1^2 = s11^2*a1^2 + s12^2*a2^2 + 2*s11*a1*s12*a2

Pref1 = rho^2*Pfor1 + (1-rho^2)*Pref2 + interference

The forward voltage equation toward the load is b2 = s21*a1 + s22*a2