"Dave" wrote in message news:7RoWh.109$Zm.79@trndny03...

"Cecil Moore" wrote in message
...
Dave wrote:
Now the big question is: Is superposition always reversible?
If not, it implies interaction between f(x) and f(y).

as long as everything is linear, yes.

This is really interesting. Given the following:

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

Let P1 = |s11(a1)|^2 = 1 joule/sec

Let P2 = |s12(a2)|^2 = 1 joule/sec

Therefore, Ptot = |b1|^2 = 0 joules/sec

Ptot = P1 + P2 + 2*SQRT(P1*P2)cos(180)

Ptot = 1 + 1 - 2 = 0 joules/sec = |b1|^2

Can one reverse the superposition whose result is
zero to recover the original two component waves?
If not, isn't that proof that the two original
component waves interacted?
--
73, Cecil http://www.w5dxp.com

no, because you have done a non-linear operation on them by converting to
powers. obviously at the start 'a1' and 'a2' are separate.


i should expand a bit more. all your equations above have done is shown
that at the point where you are doing your analysis s11(a1) and s12(a2),
which add up to 0... also produce a net 0 power at that point. this is as
expected for destructive interference AT THAT POINT. as such your s
parameter analysis is insufficient to separate the individual components
after you combine them into a power. however, at the begining they are
obviously separate waves since you have represented them with separate input
values, and given a linear transfer function for your point on the wire, or
in space, they can always be kept separate. it is only your act of
calculating the power at that point that combines them.