Roy Lewallen wrote:
Keith Dysart wrote:
On Jan 15, 2:24 am, Roy Lewallen wrote:
The little program I wrote shows that, on the line being analyzed, the
energy is changing -- moving -- on both sides of a point of zero power.
Energy is flowing into that point from both directions at equal rates,
then flowing out at equal rates. This causes the energy at that point to
increase and decrease. What zero power at a given point means is that
there is no *net* energy moving in either direction past that point.

"*net* energy moving" seems to be a bit of a dangerous notion.

If "*net* energy moving" is the time averaged power, then
it is zero at *every* point on the line under consideration.
And I do not mind this definition.

That was probably a bad choice of words on my part. By net I didn't mean
an average over some period of time. I meant energy moving past a single
point.

One possibility I envisioned was some energy moving past the point from
left to right, and at the same time an equal amount moving at the same
rate past the point from right to left, resulting in zero power at the
point. However, on reflection, this couldn't happen; energy flows
"downhill". But the phenomenon observed on the open circuited line does
occur, where energy flows into the point from both directions equally,
and out of the point to both directions equally, resulting in zero power
at the point. No energy is flowing past the point, period -- the
modifier "net" isn't necessary.

But at the points where the current or voltage is always
zero, it seems to me unnecessary to use the qualifier "*net*"
since the power IS always zero [from p(t)=v(t)*i(t)]. That
is, unless you are introducing another interpretation of
"*net*".

You're right. Please consider "net" retracted.

I got to thinking about this a little more, and want to reclaim the
"net" modifier.

Hopefully we all agree that on a line with a pure standing wave (unity
magnitude load reflection coefficient), there are nodes at which the
power is zero at all times, indicating that no (and I'll reinsert "net"
here) energy is moving past that point. But there's energy going into
that node at equal rates from both sides during half the energy cycle,
and out of the node during the other half cycle. We've used those
observations to conclude that no energy is going past the node.

But let's look at another equally plausible explanation. We know we have
a bundle of energy from the left and another equal bundle from the right
which flow into the node at the same time, resulting in zero power at
the node. But suppose that the bundle of energy from the left flows out
to the right, and the bundle from the right flows out to the left during
the next half cycle (rather than the one from the left flowing back to
the left, and the one from the right to the right, as we've been tacitly
assuming). Now we've moved energy across the node while retaining zero
power at the node (zero power because the amount of energy moving from
left to right always equals the energy moving from right to left at the
node). A nice thing about this interpretation is that it meshes neatly
with the concept of two traveling waves of equal amplitude moving in
opposite directions. Does that solve some of the conceptual problems
you've been having with the nodes?

Of course, I don't know of any way to put a tag on any particular bundle
of energy, so one explanation is really as good as the other from a
mathematical standpoint. But I think that the idea of moving the energy
past the node relieves us of the necessity, or temptation, of devising
various wave interactions to explain how the energy can just stop at the
nodes.

And, maybe it'll allow me to resurrect my *net* modifier. If you go
along with the new interpretation, energy is moving from left to right
through the node and from right to left through the node -- there is
energy moving past the node, but no *net* energy movement through the node.

Roy Lewallen, W7EL