The Rest of the Story
 

On Mar 14, 12:59*am, Cecil Moore wrote:
Keith Dysart wrote:
Cecil Moore wrote:
The difference in your energy levels is in the reactance.
The reactance stores energy and delivers it later. Why
are you having so much trouble with that age-old concept?

Show me the reactance and its power function of time such that
it stores and releases the energy at the correct time.

I don't have time to teach you AC circuit theory which
you really do need to understand. The power function
for the reactance is of the same form as it is for a
resistance, i.e. V(t)*I(t). I haven't seen you include
that reactance power function anywhere. When you do,
you will find your "missing" power and balance your
energy equations.

A fourth opportunity missed.

The reflected energy that is not dissipated in the source
resistor at time 't' is stored in the reactance and dissipated
90 degrees later. Until you choose to account for that time
delay, your energy equations are not going to balance.

I see no reactance that performs this function.

Please go take an AC circuits course. That's exactly
what a reactance does. The source terminals see +j44.1
ohms of reactance looking into the transmission line.

Yes indeed. The reactance looking into the line. But
the reflected wave is not going into the line so this
is not a reactance that it sees.

Recall, the whole premise of forward and reverse waves
is that they see the line characteristic impedance, in
these examples, a real 50 ohms with no reactance.

...Keith

The Rest of the Story
 

Keith Dysart wrote:
Yes indeed. The reactance looking into the line. But
the reflected wave is not going into the line so this
is not a reactance that it sees.

Part of the reflected wave energy is going into the
reactance along with part of the forward wave energy
when the instantaneous interference between those two
waves is destructive at the source resistor. Anything
else would violate the conservation of energy principle.
That same energy is returned to the source resistor 90
degrees later as constructive interference. Your missing
energy is in the reactance. Now you know why Hecht said
instantaneous power is "of limited utility". Where the
instantaneous energy is at any point in time is a
complicated mess that you haven't solved.

It is the average power that really matters and all the
average reflected power is dissipated in the source
resistor when the reflected wave is 90 degrees out of
phase with the forward wave but under no other conditions.

Instantaneous power is completely irrelevant to the
average power data posted on my web page. You are
saying that because my pickup has black tires, it
is not a white pickup. My article stands as written
with a disclaimer about any importance being attached
to instantaneous power.

Walter Maxwell didn't deal with instantaneous powers.
Steven Best didn't deal with instantaneous powers.
To the best of my knowledge, the instantaneous power
straw man was invented by you for the purpose of
muddying the waters.

Your instantaneous power analysis is also incorrect
because you completely ignored the instantaneous
power in the system reactance. You have completely
ignored the role of destructive and constructive
interference. You cannot possibly understand where
the energy goes until you understand interference.

We have reached the end of the discussion road and
hashed it to death. If we are still in disagreement,
we are just going to have to agree to disagree.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
This is the third opportunity you have had to clearly
identify the component and show that its energy flow
as a function of time is exactly that needed to store
and release the energy in the reflected wave.

P(t).reactance = [V(t).reactance][I(t).reactance]

Where is that term in your equations?
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
You need to read more carefully. I made no statement about
the energy incident upon port 2, only about the energy
flowing into port 2, which, after the 18 W generator is
turned on, is
Pcp2(t) = 32 + 68cos(wt)

If we have two pipes each carrying one gallon of water
per minute in opposite directions, we can agree that
the net flow of water is zero. But you are taking it
one step farther and arguing there is no water flowing
at all which is a ridiculous assertion. I'm going to
ignore this latest obvious diversion.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

On Mar 14, 8:08*am, Cecil Moore wrote:
Keith Dysart wrote:
You need to read more carefully. I made no statement about
the energy incident upon port 2, only about the energy
flowing into port 2, which, after the 18 W generator is
turned on, is
Pcp2(t) = 32 + 68cos(wt)

If we have two pipes each carrying one gallon of water
per minute in opposite directions, we can agree that
the net flow of water is zero. But you are taking it
one step farther and arguing there is no water flowing
at all which is a ridiculous assertion. I'm going to
ignore this latest obvious diversion.
--
73, Cecil *http://www.w5dxp.com

If there were two transmission lines, then I could see
why you might want two pipes in an analogy.

But since there is only one transmission line, an
analogy with one pipe makes more sense.

So you want to argue that when there is one pipe
with no water flowing, what is really happening is
that one gallon per minute is simultaneously flowing
in each direction. In the same pipe. At the same
time. I don't buy it.

You should think a bit more about
Pcp2(t) = 32 + 68cos(wt)

It is the time rate of energy flow into the port.
It can trivially be computed from the voltage and
current functions at that port.

It sums with the energy flows into the other ports
appropriately to satisfy the principle of conservation
of energy.

All is well.

And there is only one pipe for each port.

...Keith

The Rest of the Story
 

On Mar 14, 7:59*am, Cecil Moore wrote:
Keith Dysart wrote:
This is the third opportunity you have had to clearly
identify the component and show that its energy flow
as a function of time is exactly that needed to store
and release the energy in the reflected wave.

P(t).reactance = [V(t).reactance][I(t).reactance]

Where is that term in your equations?

It is unnecessary. But if you believe me wrong, show me
where it goes, compute the values, and show how it
accounts for the energy that is not dissipated in the
source resistor.

...Keith

The Rest of the Story
 

On Mar 14, 7:53*am, Cecil Moore wrote:
Keith Dysart wrote:
Yes indeed. The reactance looking into the line. But
the reflected wave is not going into the line so this
is not a reactance that it sees.

Part of the reflected wave energy is going into the
reactance along with part of the forward wave energy
when the instantaneous interference between those two
waves is destructive at the source resistor. Anything
else would violate the conservation of energy principle.
That same energy is returned to the source resistor 90
degrees later as constructive interference. Your missing
energy is in the reactance.

Still handwaving. Show the expressions and the numbers
that make it balance. Otherwise, just handwaving.

Now you know why Hecht said
instantaneous power is "of limited utility".

I've known that for quite a while. It is because it is so
difficult to measure with optical signals.

Where the
instantaneous energy is at any point in time is a
complicated mess that you haven't solved.

Not at all. Follow the spreadsheet for a full accounting.

It is the average power that really matters and all the
average reflected power is dissipated in the source
resistor when the reflected wave is 90 degrees out of
phase with the forward wave but under no other conditions.

Averaging is a mathetical operation applied to a function.
In this case a function of time.

The underlying function of time conveys more information than
does just the average which is why just dealing with averages
can lead one astray.

Instantaneous power is completely irrelevant to the
average power data posted on my web page.

Well, it does disprove some of your claims so I can see
why you like to belittle it.

You are
saying that because my pickup has black tires, it
is not a white pickup. My article stands as written
with a disclaimer about any importance being attached
to instantaneous power.

See previous comment.

Walter Maxwell didn't deal with instantaneous powers.
Steven Best didn't deal with instantaneous powers.
To the best of my knowledge, the instantaneous power
straw man was invented by you for the purpose of
muddying the waters.

Your instantaneous power analysis is also incorrect
because you completely ignored the instantaneous
power in the system reactance. You have completely
ignored the role of destructive and constructive
interference. You cannot possibly understand where
the energy goes until you understand interference.

I observe that you have not provided any expansion
based on either reactance or interference that accounts
for the differences.
Most probably because it is not possible.

We have reached the end of the discussion road and
hashed it to death. If we are still in disagreement,
we are just going to have to agree to disagree.

Are you really going to let me be the last man standing
this time?

We shall see.

...Keith

The Rest of the Story
 

Keith Dysart wrote:
If there were two transmission lines, then I could see
why you might want two pipes in an analogy.

But since there is only one transmission line, an
analogy with one pipe makes more sense.

Unfortunately for your argument, molecular water and
EM waves are considerably different animals. Water
energy traveling in opposite directions in a pipe
interact. EM waves traveling in opposite directions
in a transmission line interact only at an impedance
discontinuity or at an impedor. As long as only a
constant Z0 environment exists, the forward wave and
reflected wave pass like ships in the night. For you
to prove otherwise, you are going to have to define
the position and momentum of a single photon. Good
luck on that one.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
On Mar 14, 7:59 am, Cecil Moore wrote:
P(t).reactance = [V(t).reactance][I(t).reactance]
Where is that term in your equations?

It is unnecessary. But if you believe me wrong, show me
where it goes, compute the values, and show how it
accounts for the energy that is not dissipated in the
source resistor.

It is unnecessary to account for all of the instantaneous
power???? Your problem is greater than just a simple
misunderstanding of the laws of physics by which we must
all abide.

The DC energy is stored in your vehicle's battery until
it is needed to start your vehicle. That delay between
stored energy and needed energy is related to the
(undefined) wavelength. Think about it.

In an AC circuit, the reactance has no say as to when
to store the energy and when it is delivered back to the
system. It is also related to wavelength which is defined.

When the source voltage is zero at its zero crossing
point/time, the instantaneous power dissipation in
the source resistor is NOT zero! Doesn't that give
you pause to wonder where the instantaneous power
is coming from when the instantaneous power delivered
by the source is zero???? Why do you ignore that power
and try to sweep it under the rug?

You are making the mistakes that your EE 201 professor
warned you not to make. You are superposing powers,
something that all the gurus on this newsgroup will
condemn. Until you learn not to superpose powers, you
will remain forever ignorant. Richard C. made the same
mistake when he declared that the reflections from non-
reflective thin-film coatings on glass are "brighter
than the surface of the sun". If one ignores the laws
of physics, anything is possible.

There is a condition where it is valid to superpose
powers. That is when (V1^2 + V2^2) = (V1 + V2)^2
You have obviously not satisfied that condition and
are paying for your violations of those laws of physics.
Until you give up on your superposition of powers, I
cannot help you.
--
73, Cecil http://www.w5dxp.com

The Rest of the Story
 

Keith Dysart wrote:
Still handwaving. Show the expressions and the numbers
that make it balance. Otherwise, just handwaving.

Show the expressions and the numbers for how many angles
can dance on the head of a pin???? Shirley, you jest.
This is not the proper venue to try to establish your
new religion.

Are you really going to let me be the last man standing
this time?

No, you died in action a few weeks ago and don't realize
it. It happened the first time you superposed powers when
(V1^2 + V2^2) is not equal to (V1 + V2)^2. Too bad you
are incapable of comprehending exactly what that means.
You can easily work it out for yourself but you haven't
yet attempted to do so. Hopefully, one of the resident
gurus whom you trust will explain it to you.

Until you correct your ignorance on that subject, *you* are
just handwaving. I suggest you contact someone who is more
knowledgeable than you on the subject. Ask Richard C. to
prove his assertion that the reflections from a non-reflective
thin-film surface are brighter than the sun. If you detect
what is wrong with his argument, you will know what is wrong
with yours.
--
73, Cecil http://www.w5dxp.com