On Apr 8, 8:51*am, Cecil Moore wrote:
Roy Lewallen wrote:
Now, I don't know of any way to assign "ownership" to bundles of energy.

One way is to add a unique bit of modulation to each
bundle of wave energy. I am fond of using a TV signal
and observing ghosting on the screen. This, of course,
assumes that the modulation stays with the same component
wave to which it was originally associated.

But as soon as you modulate, you no longer have sinusoidal
steady state.

You can split the signal up into its spectral components
and, using superposition, analyze the circuit for each
spectral component individually, then sum them to obtain
the total system response. But chasing the energy with
one frequency is hard enough. The conundrums that arise
when doing it for several are much worse than the ones
here.

For your enjoyment consider the composite signal
cos(9.95*2*pi*t)+cos(10.05*2*pi*t)
working into 1 ohm.
The imputed average power for each of the components is
0.5 W. The total average power is 1 W as expected.

Consider the 1 second interval from 4.5 to 5.5 seconds.
In this second 0.016393 joules flow for an average
power of 0.016393 W. But the sum of the imputed power
in the two spectral components is 1 W. Where did the
missing energy go?

Just another example of why assigning too much reality
to the imputed powers of the components of superposition
is misleading.

But let's suppose that the energy which flows into the node from the
left side during the "inhalation" part of the cycle is the energy which
flows out to the right during the "exhalation" part of the cycle, and
the energy flowing into the node from the right exits on the left. So
now we've managed to get energy past the node going in both directions
while maintaining zero power and current at the node and conserving
energy as we must.

This agrees with the distributed network model. Since
there is no impedance discontinuity and no impedor at
the node, there can be no reflections at the node.

In other examples, you have suggested inserting a zero length
transmission line to aid analysis. Why not insert a zero length
transmission line with an impedance to produce the desired
reflection? At steady state the reflection cancels but this
would be due to the redistribution of energy according to
your explanations.

The
forward wave flows unimpeded through the node as does
the equal magnitude reflected wave. The net energy flow
is zero. The average energy flow is zero.

Anyone who believes there is zero energy at a standing-
wave current node should touch that point on a transmission
line (which just happens to be the same point as the
maximum voltage anti-node).

No one has said there is zero energy. Only that there is
zero energy flow. For energy flow, one needs simultaneous
voltage and current.

One must be careful not to confuse the net signal with the
component signals.

Agreed. Assigning too much reality to component signals is
seriously misleading. Now actual voltages, currents and
powers, that's a different thing.

One must be careful not to confuse the
average values with the instantaneous values.

This can best be visualized using light waves in free
space. Unimpeded EM waves do not bounce off of each other.

Until one can grasp the simplicity of a transmission line,
moving to the complexity of free space offers nothing but
obfuscation.

...Keith