On Mar 4, 8:00*pm, Keith Dysart wrote:
On Mar 4, 3:36*pm, Cecil Moore wrote:

After discovering the error on Roy's web page at:

http://eznec.com/misc/Food_for_thought.pdf

I have begun a series of articles that convey "The Rest
of the Story" (Apologies to Paul Harvey). Part 1 of
these articles can be found at:

http://www.w5dxp.com/nointfr.htm

Looks good. And well presented. There is only one small problem
with the analysis.

When the instantaneous energy flows are examined it can be seen
that Prs is not equal to 50 W plus Pref.

Taking just the second example (12.5 ohm load) for illustrative
purposes...

The power dissipated in Rs before the reflection arrives is
Prs.before = 50 + 50cos(2wt) watts

The reflected power at the source is
Pref.s = 18 + 18cos(2wt) watts

But the power dissipated in Rs after the reflection arrives is
Prs.after = 68 + 68cos(2wt-61.9degrees) watts

Prs.after is not Prs.before + Pref, though the averages do sum.

And since the energy flows must be accounted for on a moment by
moment basis (or we violate conservation of energy), it is the
instantaneous energy flows that provide the most detail and
allow us to conclude with certainty that Prs.after is not
Prs.before + Pref.

The same inequality holds for all the examples except those
with Pref equal to 0.

Thus these examples do not demonstrate that the reflected power
is dissipated in the source resistor.

...Keith

I should have mentioned that there are some energy flows that do
add, as expected.

The energy delivered by the generator to the line (or equivalently,
the energy flowing in the line at the generator end) is the sum
of the forward and reverse energy flows...

Pf.g = 50 + 50cos(2wt)
Pr.g = -18 + 18cos(2wt)
Pline.g = 32 + 68cos(2wt)

And the energy delivered by the source is always equal to the
energy being dissipated in the resistor plus the energy being
delived to the line...

Prs = 68 + 68cos(2wt-61.9degrees)
Rline.g = 32 + 68cos(2wt)

Psource = 100 + 116.6cos(2wt-30.96degrees)

Psource is equal to Prs + Pline.g

So the energy flows that should add up, do add up.

...Keith