On Mar 25, 8:23 pm, Cecil Moore wrote:
You are not allowed to deny the existence of the 450 ohm
real world load while asserting that it still exists.
If it exists, it dissipates the reflected energy. If it
doesn't exist, it reflects the reflected energy. Please
choose one or the other - obviously, you cannot have both
at the same time.
[snip]
If reflected energy is not dissipated, it undergoes destructive
interference and is redirected back toward the load as constructive
interference instead of being incident upon the source.

I like these two paragraphs. They describe exactly what
I would expect the relationships to be were "reflected
energy" to represent real energy.

More importantly, they describe an expectation that
is sufficiently precise to be falsifiable.

But just to be sure I understand the meaning, let me restate
them algebraically:
Energy.reflected = Energy.dissipated + Energy.re-reflected

If this is not what you meant, then please read no further
until you correct my misinterpretataion.

----

Oh good. The interpretation is accepted. So let us call
this "Cecil's Hypothesis":
"If reflected energy is not dissipated, it is redirected
back toward the load."
Expressed as an equality:
Energy.reflected = Energy.dissipated + Energy.re-reflected
And for convenience, its power form:
Preflected = Pdissipated + Pre-reflected

Now all we need is a single example for which the equality
does not hold and "Cecil's Hypothesis" will be disproved.

Let us start with the example previously offerred:
- Generator with 450 Ohm output impedance
- connected directly to a 1000 foot line with 450 Ohm
characteristic impedance
- connected to a load with 75 Ohm input impedance.

And to simplify computation and produce a numerical
result, we add a few more details:
- The generator is 2 Amp current source in parallel with
a 450 Ohm resistor
- The line is 31 wavelengths long

Let the experiment begin:
- The generator is off.
- All currents, voltages, energies and powers are zero.
- Turn on the current source.
- The current source pushes 2 Amps.
- This is divided equally between the 450 Ohm generator
resistor and the 450 Ohm line.
- The generator output voltage is 450 Volts.
- The generator output current is 1 Amp.
- 450 Watts is being put out by the generator
- 450 Watts is being dissipated in the generator resistor
- A real wattmeter (one that measures voltage and current)
shows 450 Joules/s flowing down the line. (Is it okay to
say that "450 Watts are flowing"?)
- A directional wattmeter indicates that the "forward
power" is 450 Watts and the "reflected power" is 0
Watts.
- Vfwd is 450 Volts
- Ifwd is 1 Amp
- The load is happily oblivious to the oncoming onslaught.
- 31 cycles later, the voltage, current and energy reach
the load.
- But there is an impedance discontinuity which creates
a voltage reflection coefficient of -0.714 so the load
refuses to accept all the incoming energy.
- The voltage across the load is 128.6 Volts
- The current into the load is 1.714 Amps
- The power dissipated in the load is 220.4 Watts
- Vref is -321.5 Volts
- Iref is 0.714 Amps
- Vfwd is still 450 Volts (the line is lossless for this
example)
- Ifwd is still 1 Amp
- "Forward power" is 450 Watts
- "Reflected power" is 229.6 Watts
- 220.4 = 450 - 229.6 which is as expected and
demonstrates the usefullness of a directional wattmeter
for computing actual power transferred (or is it energy?).
- Encountering the reflection has caused a change in
the voltage and current and this change is now
propagating back towards the generator.
- 31 cycles later, this change in line conditions
reaches the generator.
- The conditions at the generator terminals are now
the same as the load since it is an integral number
of wavelengths from the load.
- The voltage at the generator terminals is 128.6 Volts
- The current out of the generator is 1.714 Amps
- The "forward power" is still 450 Watts.
- The "reflected power" has changed from 0 to 229.6
Watts.
- There is 128.6 volts across the 450 Ohm generator
resistor.
- There is 0.286 Amps flowing in the 450 Ohm generator
resistor
- Because the 0.286 Amps in the 450 Ohm generator
resistor plus the 1.714 Amps flowing into the line
is 2 Amps, exactly the output of the current source,
the system has now settled after one round trip.
There is no re-reflection at the generator
terminals (and no ghosts).
- The power into the line is 220.4 Watts
- The power into the 450 Ohm generator resistor is
38.6 Watts
- 229.6 Watts of "reflected power" has reduced the
dissipation in the generator resistor by 413.4 Watts.
- Substituting into the hypothetical equality
Preflected = Pdissipated + Pre-reflected
229.6 = -413.4 + 0
- The equality does not hold, thus disproving
"Cecil's Hypothesis".

It is instructive to also consider the case with a
generator constructed as a 900 Volt voltage source
connected to a 450 Ohm output resistor.

In this case the 450 Watts dissipated for the first
62 cycles increases by 872 Watts to 1322 Watts when
the reflection arrives. Similar to above there is
no re-reflection or ghosts.

Once again the hypothetical equality
Preflected = Pdissipated + Pre-reflected
229.6 = 872 + 0
does not hold.

But the principle of "conservation of energy" should
hold whenever real energies are involved.
Since it does not hold in this case, we can only
conclude that the numbers computed for "forward and
reverse power" do not represent any real energy flows
but are merely conveniences to facilitate other
computations.

....Keith