Dave wrote:
so roy has correctly calculated the standing wave 'power' to be zero at two
points on the line. i am sure that yuri will take great exception to this
result showing there is no power in the standing wave.

but he missed the definition of pr and pf...

dave in problem statement:
now, calculate vf(t), if(t),pf(t), vr(t), ir(t), pr(t) at that point,
where
the 'f' terms are the forward wave, the 'r' terms are the reflected wave.

so he conveniently skipped that step and instead writes this cop out:

roy:
I haven't seen a definition of pr and pf, but they're not relevant to
the discussion. If you get a different result for power than zero by
using whatever you take them to mean, then the concept is invalid.

pr and pf are, as i stated, the power in the forward and reflected waves.
There is of course power in these two waves and it is indeed 'sloshing' back
and forth in the line. These are the waves that can be measured by any of
the simple devices such as neon bulbs or bird watt meters that clearly show
equal and opposite powers in the waves. so you can indeed have power in the
traveling waves, but no power in the standing waves... which will always be
the case.

i will give him this point as being correct for a lossless open (or shorted)
line:

There
is no average power leaving the source and no average power being
dissipated in the load(*). So there had better be no average power
anywhere in the line.

but then he loses it again:

There will be non-zero instantaneous power
everywhere along the line except at the input, far end, and midway, but
its average value will be zero,

the traveling waves will have power EVERYWHERE on the line, the special
cases are are just the ones where the standing wave is most easily shown as
having no power. obviously if there is power in a wave at one point on a
line it is not going to stop and bypass the quarter wave points, the forward
and reflected waves continue end to end and their power goes with them... it
is at those 'special' points where the voltage or currents in the forward
and reflected waves always cancel each other so if you measure with a simple
tool you will see the voltage or current nulls at those points. that does
not mean there is no power passing those points, only that the voltage or
current in the traveling waves has conveniently canceled each other out at
those points.

and then he has to end up with an obvious contradiction:

indicating the movement of energy back
and forth but no net energy flow.

how does energy not flow if it is moving back and forth???




I see we are back to the old business about colliding waves that
apparently carry vector power. At least it seems that way since the
counter-traveling power can cancel at some points and add up at other
points. I thought we trashed this idea a couple of years ago.

Remember, calculate fields first and then worry about power or energy.
Any change in that calculation order will surely lead to "traveling
waves of average power" and other such gems.

I hope no Joules are hurt in the collision.

73,
Gene
W4SZ