Keith Dysart wrote:
So, contrary to Cecil's assertion, an analysis based on
'no reflections at the source', has not resulted in any
violation of conservation of energy. This is good.

Again your analysis violates the conservation of energy
principle. The only way to balance your energy equation
is for your source to supply 25 joules/sec.

IF THE REFLECTED WAVE IS NOT REFLECTED FROM THE SOURCE,
IT FLOWS THROUGH THE SOURCE RESISTOR AND IS DISSIPATED
IN THE SOURCE RESISTOR. THAT REFLECTED WAVE ENERGY IS
THEREFORE NOT AVAILABLE TO THE FORWARD WAVE.

You cannot eat your reflected wave and have it too.

The standard equation is:

Psource = Pfor - Pref = Pload

But you have taken away the reflected energy and
dissipated it in the source resistor. So your new
equation becomes:

Psource = Pfor + ????????
18.75w = 25w + ________

You say the source power is 18.75 joules/sec and the
forward power is 25 joules/sec. If none of the reflected
energy is available to the forward wave, where did the
extra 6.25 joules/sec come from? Is it sheer coincidence
that the reflected wave is associated with 6.25 joules/sec
that are now missing from the above equation?

Here is an example of the reflected wave flowing through
a circulator resistor and being dissipated.

Source---1---2----45 deg 50 ohm feedline---150 ohm load
25w \ / 18.75w
|
50 ohms
6.25w

But in this example Psource = Pfor in order to satisfy
the conservation of energy principle which your example
does not.
--
73, Cecil http://www.w5dxp.com

On Feb 5, 10:44*am, Cecil Moore wrote:
Keith Dysart wrote:
So, contrary to Cecil's assertion, an analysis based on
'no reflections at the source', has not resulted in any
violation of conservation of energy. This is good.

Again your analysis violates the conservation of energy
principle. The only way to balance your energy equation
is for your source to supply 25 joules/sec.

IF THE REFLECTED WAVE IS NOT REFLECTED FROM THE SOURCE,
IT FLOWS THROUGH THE SOURCE RESISTOR AND IS DISSIPATED
IN THE SOURCE RESISTOR. THAT REFLECTED WAVE ENERGY IS
THEREFORE NOT AVAILABLE TO THE FORWARD WAVE.

Not sure that shouting helps. I do not find any unbalances
with the energy. See below.

You cannot eat your reflected wave and have it too.

The standard equation is:

Psource = Pfor - Pref = Pload

Yes. Indeed. And just changing to use my terminology...

Pgenerator = Pfor - Pref = Pload

For the example at hand...

Pgenerator = 18.75
Pfor - Pref = 18.75
Pload = 18.75

And the source provides 50 W of which 31.25 is dissipated
in the source resistor and 18.75 is delivered to the
line (Pgenerator, above).

All seems well with world and no energy is left unaccounted.

But you have taken away the reflected energy and
dissipated it in the source resistor. So your new
equation becomes:

Psource = Pfor + ????????
18.75w *= 25w *+ ________

As your original equation above

Psource = Pfor - Pref
18.75 = 25 - 6.25

I do not see any issues.

When the source was first turned on, 25 J/s flowed from
the generator into the line.
Pfor = 25 W

After the reflected wave makes it back to the generator,
25 - 6.25 - 18.75 J/s are flowing in the line.
Pfor - Pref = 18.75 W

And the generator output has also reduced from 25 W to
18.75 W, so all is still in balance.

I am having difficulty determining where you think there
is a violation of the conservation of energy principle.

...Keith

PS Do not be fooled by the numerology where 25 + 6.25
gives 31.25. For the 35 degree line, the corresponding
numbers are
Ps = 41.449507
Prs = 22.699502
Pg = 18.75
Pf = 25
Pr = 6.25
Pl = 18.75

Pg = Pf - Pr = Pl
Ps = Prs + Pg
All as expected. No missing energy.