Standing-Wave Current vs Traveling-Wave Current
 

On Jan 12, 4:24*pm, Cecil Moore wrote:
On Jan 12, 3:25 pm, Keith Dysart wrote:

But, of course, V(t) and I(t) are general functions
of time. In particular, the discusion was regarding
pulses.

Pulses can be analyzed as Fourier sinusoidal functions with multiple
frequencies. Point is that you could have saved a month of grief on
this newsgroup if you had initially said your power equation applied
only to real voltage and real current. If you had done that, nobody
would have argued with you.

An earlier post suggested that you "had got it", but these
last two posts leave me wondering.

P(t) = V(t) * I(t)
where V(t) and I(t) are functions describing the actual
measureable voltage and current at a point on the line.

Examples of V(t) would be
V(t) = 10
V(t) = A cos(wt + a)

These functions all yield real results since the voltage
measureable at a point on the line is a real function
of time.

When the latter example is written in complex exponential
form it becomes
V(t) = Re[A*e^j(wt+a)]

Re[] is not there because there is some imaginary part
to be ignored, but because this is how one writes the
function for V(t) in this notation.

Thus Re[V(t)] is non-sensical since the Re[] is already
in the expression describing the function.

My apologies for not detecting this subtle bit of
misleading thinking when I wrote my earlier reply.

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 12, 8:45 pm, Keith Dysart wrote:
P(t) = V(t) * I(t)
where V(t) and I(t) are functions describing the actual
measureable voltage and current at a point on the line.

Apparently, the measurable *instantaneous* voltage and current. We
could have avoided a lot of wasted time if you had stated those
conditions a month ago. None of my references contain that equation.

Re[] is not there because there is some imaginary part
to be ignored, but because this is how one writes the
function for V(t) in this notation.

Where is it? You have never explained your assumptions before now.
Please provide a reference.
--
73, Cecil, w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 12, 11:23*pm, Cecil Moore wrote:
On Jan 12, 8:45 pm, Keith Dysart wrote:

P(t) = V(t) * I(t)
where V(t) and I(t) are functions describing the actual
measureable voltage and current at a point on the line.

Apparently, the measurable *instantaneous* voltage and current. We
could have avoided a lot of wasted time if you had stated those
conditions a month ago. None of my references contain that equation.

I am curious. What other interpretation than 'voltage as a
function of time' did you have for "V(t)"?

And, of course, when you plug any particular time into a
function describing xxxx as a function of time, you get
the value of xxxx at that time; the instantaneous value
of xxxx.

Or is there another possible interpretation?

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 13, 7:58 am, Keith Dysart wrote:
I am curious. What other interpretation than 'voltage as a
function of time' did you have for "V(t)"?

Strange question. My interpretation is not the "other interpretation".
My interpretation is the (apparently) standard one from "Fields and
Waves", by Ramo&Whinnery - begin quote:

V(t) = Re[Vm*e^jwt]

Because of the inconvenience of this notation, it is usually not
written explicitly but is understood. - end quote

When you used the term, "V(t)", I understood it to represent the
Ramo&Whinnery definition applying to exponential notation. Your
interpretation is the one that differs from that definition. What
other interpretation than the Ramo&Whinnery equation do *YOU* have for
V(t)?

Or is there another possible interpretation?

Apparently there is and you can prove it by providing a reference that
extends V(t) in the Ramo&Whinnery definition above to something other
than exponential notation. I am not doubting your word, just (pretty
please) asking again for a reference that agrees with your statement
that V(t) is used for something else.

If "V(t)" is commonly used outside of the Ramo&Whinnery definition
above, I apologize for being confused by the notation being used.
--
73, Cecil, w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 13, 8:54*am, Cecil Moore wrote:
If "V(t)" is commonly used outside of the Ramo&Whinnery definition
above, I apologize for being confused by the notation being used.

Apology accepted. As a cautionary note....
It is unwise to take the notation used in one text and blindly
substitute into another, especially when the text is deriving
for a specific case.

The IEEE dictionary (see 'instantaneous power') starts with
p = ei
and then goes on to derive the special case for sinusoids.

Desoer and Kuh, "Basic Circuit Theory", start with
p(t) = v(t)i(t)
then derive the special case for sinusoids by substituting
v(t) = Vm * cos(wt+a) = Re[Vm * e^ja * e^jwt] {taking some liberties
to make it ascii}
Note that Re[] is only needed when using the exponential form
and not the trigonometric form.

And, from your post, it appears that Ramo and Whinnery start with
W(t) = V(t) I(t)
and do the derivation for the special case of sinusoids by
substituting
V(t) = Re[Vm*e^j(wt+A1)]

These are all equivalent derivations using different notations.

A key point is that they all start with "instanteous power
being equal to instantaneous voltage times instantaneous current"
as the general case and derive the special case by appropriate
substitution.

And a second key point is that Re[] is not needed in the general
expression for power, (choose the form you like)
p = ei
p(t) = v(t) i(t)
P(t) = V(t) I(t)
, because it is already in the expressions for voltage and current
when the exponential form is used.

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 13, 12:02 pm, Keith Dysart wrote:
It is unwise to take the notation used in one text ...

Unfortunately, I only brought one book with me. Ramo&Whinnery don't
discuss non sinusoidal signals. Even their square waves are analyzed
as a Fourier series whose total voltage is f(t), not V(t).
--
73, Cecil, w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:

You don't need Poynting vectors to realize that when
the instantaneous power is always 0, no energy is flowing.
And when the instantaneous power is always 0, it is
unnecessary to integrate and average to compute the
net energy flow, because no energy is flowing at all.

And if by your response you really do mean that energy
can be flowing when the instantaneous power is always 0,
please be direct and say so.

But then you will have to come up with a new definition
of instantaneous power for it can not be that it is
the rate of energy transfer if energy is flowing when
the instantaneous power is zero.

The little program I wrote shows that, on the line being analyzed, the
energy is changing -- moving -- on both sides of a point of zero power.
Energy is flowing into that point from both directions at equal rates,
then flowing out at equal rates. This causes the energy at that point to
increase and decrease. What zero power at a given point means is that
there is no *net* energy moving in either direction past that point.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
...
What zero power at a given point means is that
there is no *net* energy moving in either direction past that point.

Roy Lewallen, W7EL

A black hole? :-D

JS

Standing-Wave Current vs Traveling-Wave Current
 

Comments interspersed. . .

Keith Dysart wrote:
Thanks for offering the two capacitor/one capacitor view of the middle
of the line. It took a bit of time to decide whether the commingling
of the charge in the single capacitor at the middle of the line would
solve my dilemma.

So I considered this one capacitor in the exact center of a perfect
transmission line. It is the perfect capacitor, absolutely
symmetrical. So as the exactly equal currents flow into it on
the exactly symmetrical leads, the charge is perfectly balanced
so that the charge coming from each side exactly occupies its
side of the conductor. As the two flows of charge flow over
the perfectly symmetrical plates, they meet in the exact
center, and flow no more. I conclude that a surface can
be found exactly in the center of this capacitor across
which no charge flows. Thus (un)happily returning me exactly
to where I was before; there is a line across which no
charge, and hence no energy, flows.

I'm ok with that. To me, it's the same as splitting the capacitor into
two separate ones, each with its own charge from one direction.

More comments below.

On Jan 2, 7:38 pm, Roy Lewallen wrote:
I'm top posting this so readers won't have to scroll down to see it, but
so I can include the original posting completely as a reference.

Keith, you've presented a very good and well thought out argument. But
I'm not willing to embrace it without a lot of further critical thought.
Some of the things I find disturbing a

1. There are no mathematics to quantitatively describe the phenomenon.
2. I don't understand the mechanism which causes waves to bounce.

I take this to imply that you are not happy with the simple "like
charge
repels"?

That's right. Although it's a true statement, I haven't seen any
explanation of why it would cause waves to bounce off each other.

3. No test has been proposed which gives measurable results that will
be different if this phenomenon exists than if it doesn't. (I
acknowledge your proposed test but don't believe it fits in this category.)
4. I'm skeptical that this mechanism wouldn't cause visible
distortion when dissimilar waves collide. But without any describing
mathematics or physical basis for the phenomenon, there's no way to
predict what should or shouldn't occur.
5. Although the argument about no energy crossing the zero-current
node is compelling, I don't feel that an adequate argument has been
given to justify the wave "bouncing" theory over all other possible
explanations.

I would really appreciate seeing some other possible explanations.

How about this: During the initial turn-on of the system, energy does
cross the magic node. It's only in the theoretical limiting case of
steady state that the energy goes into and out of the node but doesn't
cross it. I'll argue that the limiting case can never be reached --
since this whole setup is a perfect construct to begin with. Or, if
that's not adequate by itself, what's the problem with energy being
trapped between nodes once the line is charged and steady state is reached?

One other one which I have seen and am not confortable with is the
explanation that energy in the waves pass through the point in
each direction and sum to zero. But this is indistinguishable from
superposing power which most agree is inappropriate. As well, this
explanation means that P(t) is not equal to V(t) times I(t),
something that I am quite reluctant to agree with.

I won't go there either.

The other explanation seen is that the voltage waves or the
current waves travel down the line superpose, yielding a total
voltage and current function at each point on the line which
can be used to compute the power.

This is done and graphically shown with the TLVis1 program demo. The
energy at each point is also calculated and shown.

With this explanation, P(t)
is definitely equal to V(t) time I(t), which I do appreciate.
The weakness of this explanation is that it seems to deny
that the wave moves energy. And yet before the pulses collide
it is easy to observe the energy moving in the line, and if
a pulse was not coming in the other direction, there would
be no dispute that the energy travelled to the end of the
line and was absorbed in the load. Yet when the pulses
collide, no energy crosses the middle of the line. Yet
energy can be observed travelling in the line before
and after the pulses collide.

I think the basic problem here is assigning energy to each traveling
wave. It's taking you into exactly the same morass that Cecil constantly
finds himself in. He also concluded some time back that two waves which
collide had to reverse direction in order to conserve power, energy,
momentum, or something. Energy in the system is conserved; but nowhere
is it written that each wave has to have individually conserved energy.

So...

I can give up on pulses (or waves) moving energy. I am not
happy doing that.

I'm afraid you might have to.

I can give up on P(t) = V(t) * I(t). I am not happy doing
that either.

Fortunately, that's not necessary.

So the (poorly developped) "charge bouncing" explanation
seems like a way out, but I certainly would appreciate
other explanations for consideration.

I think you need to take a closer look at what it's getting you out
from. I believe the problem lies there.

None of these make an argument with your logical development, although I
think I might be able to do that too. But I'm very reluctant to accept a
view of wave interaction that's apparently contrary to established and
completely successful theory and one, if true, might have profound
effects on our understanding of how things work. So frankly I'm looking
hard for a flaw in your argument. And I may have found one.

So I am not convinced that it any way goes against established theory.
I have not seen established theory attempt an explanation of how the
waves can both transport energy as well as not do so when waves of
equal energy collide.

Perhaps that's because individual waves don't transport energy that has
to be conserved?

. . .


It would be instructive to see what happens as, for example, the load
resistance is increased toward infinity or decreased toward zero
arbitrarily closely, but not at the point at which it's actually there.
If the "bouncing" phenomenon is necessary only to explain the limiting
case of infinite SWR on a perfect line but no others, then an argument
can be made that it's not necessary at all. I suspect this is the case.

The same concern that arises for pulses of equal voltage also
occurs for pulses of different voltage. While the mid-point no
longer has zero current, the actual current is only the difference
of the two currents in the pulses, the charge that crosses is only
the difference in the charge between the two pulses, and the
power at the mid-point is exactly the power that is needed
to move the difference in the energy of the two pulses.

Sorry, I'm having trouble following that. Voltage, current, charge, and
energy all in two sentences has too high a concept density for me to handle.

So the challenge is not so starkly obvious as it is when the
power at the mid-point is always 0, but P(t) = V(t) * I(t) can
still be computed and it will not be sufficient to allow
the energy in the two pulses to cross the mid-point (unless
one likes superposing power, in which case it will be
numerologically correct).

No, it'll have to be done without superposing power. Simple calculations
clearly show where the power is and where the energy is going, without
the need to superpose power or assign power or energy to individual waves.

I agree with your argument about two sources energized in turn, and have
used that argument a number of times myself to refute the notion of
superposing powers. Once two voltage or current waves occupy the same
space, the only reality is the sum. We're free to split them up into
traveling waves or any other combination we might dream up, with the
sole requirement being that the sum of all our creations equals the
correct total. (And the behavior of waves you're describing seemingly go
beyond this.)

I sometimes think that this may actually be a debate about the
conceptual view of waves. If waves consist only of voltage and
current, then all is well, superposition works, the correct
answers are achieved. And if the power is computed after the
voltages and currents are arrived at, all is well.

But if one conceives waves as also including energy, then it
seems that the question 'where does the energy go' is valid
and the common explanations do not seem to hold up well.

I think you're partially right about that. Partially, because I think
there's an underlying assumption that the power in an individual wave
has to be conserved. If you do insist on assigning energy to individual
traveling waves, I think you have to be willing to deal with the fact
that the energy can be swapped and shared among different waves, and
stored and returned as well.

Our common analytical techniques deal with E and H fields which we can
superpose. In a transmission line, these are closely associated with
voltages and currents. They add nicely to make a total with properties
we can measure and characterize, and the total can neatly be created as
the sum of individual traveling waves from turn on until steady state.
It all works very well. Two fields, voltages or currents can easily add
to zero simply by being oriented in opposite directions -- and they do,
all along a transmission line. But how are the energies they supposedly
contain going to add to zero? You'll have to construct a whole new model
if you're going to require conservation of energy of individual
traveling waves. I'm absolutely certain that after all the work of
developing a self-consistent model with all interactions quantitatively
and mathematically explained and accounted for, we'll find a testable
case where some measurable result will be different from the
conventional viewpoint. (Google "ultraviolet catastrophe".) That would
then establish the validity of the new model. But I'm just as certain
that no such mathematical model will ever be forthcoming.

The advantage to the non-interacting traveling wave model
is that it so neatly predicts transient phenomena such as TDR and run-up
to steady state. I spent a number of years designing TDR circuitry,
interfacing with customers, and on several occasions developing and
teaching classes on TDR techniques, without ever encountering any
phenomena requiring explanations beyond classical traveling wave theory.
So you can understand my reluctance to embrace it based on a problem
with energy transfer across a single infinitesimal point in an ideal line.

Yes, indeed. Though any (new) explanation would have to remain
consistent with the existing body of knowledge which works so well.

Either that, or be able to demonstrate where the existing knowledge
fails. I'm not holding my breath.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
What zero power at a given point means is that
there is no *net* energy moving in either direction past that point.

Exactly! But that does not preclude the forward Poynting vector
being equal in magnitude to the reflected Poynting vector.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
I think the basic problem here is assigning energy to each traveling
wave. It's taking you into exactly the same morass that Cecil constantly
finds himself in. He also concluded some time back that two waves which
collide had to reverse direction in order to conserve power, energy,
momentum, or something. Energy in the system is conserved; but nowhere
is it written that each wave has to have individually conserved energy.

I wish you would stop using you guru status to misquote people.
During wave cancellation, the waves do *NOT* "collide". They
cannot collide since they are traveling in the same direction.
I just read on a plane trip today where Ramo & Whinnery talk
about wave cancellation. When waves are canceled, their energy
components have to go somewhere.

I disagree with Roy's last sentence. If an EM wave exists, it's
Poynting vector is ExM. The energy in that individual wave *must*
be conserved. If that energy is not conserved, the conservation
of energy principle is violated.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

If an EM wave exists, it's
Poynting vector is ExM. The energy in that individual wave *must*
be conserved. If that energy is not conserved, the conservation
of energy principle is violated.

When a wave is canceled, there is no wave. Therefore there can be no
energy associated with that wave. If there is energy, then it must be
associated with a wave that is not canceled. Same thing is true when
I have candy. If it's not in my left hand, then it must be in my
right hand. It's all very profound.

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
When a wave is canceled, there is no wave.

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are
180-degrees ... out of phase with each other meet, they are not
actually annihilated, ... All of the photon energy present in
these waves must somehow be recovered or redistributed in a new
direction, according to the law of energy conservation ... Instead,
upon meeting, the photons are redistributed to regions that permit
constructive interference, so the effect should be considered as
a redistribution of light waves and photon energy rather than
the spontaneous construction or destruction of light."

The canceled waves are "not annihilated" even though there is, as
you say, no wave in the direction of cancellation. The energy in
the canceled waves is "redistributed" in the opposite direction
in the transmission line as constructive interference. We hams call
that event a "reflection".
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 15, 2:24*am, Roy Lewallen wrote:
Keith Dysart wrote:

You don't need Poynting vectors to realize that when
the instantaneous power is always 0, no energy is flowing.
And when the instantaneous power is always 0, it is
unnecessary to integrate and average to compute the
net energy flow, because no energy is flowing at all.

And if by your response you really do mean that energy
can be flowing when the instantaneous power is always 0,
please be direct and say so.

But then you will have to come up with a new definition
of instantaneous power for it can not be that it is
the rate of energy transfer if energy is flowing when
the instantaneous power is zero.

The little program I wrote shows that, on the line being analyzed, the
energy is changing -- moving -- on both sides of a point of zero power.
Energy is flowing into that point from both directions at equal rates,
then flowing out at equal rates. This causes the energy at that point to
increase and decrease. What zero power at a given point means is that
there is no *net* energy moving in either direction past that point.

"*net* energy moving" seems to be a bit of a dangerous notion.

If "*net* energy moving" is the time averaged power, then
it is zero at *every* point on the line under consideration.
And I do not mind this definition.

But at the points where the current or voltage is always
zero, it seems to me unnecessary to use the qualifier "*net*"
since the power IS always zero [from p(t)=v(t)*i(t)]. That
is, unless you are introducing another interpretation of
"*net*".

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 15, 6:03*am, Roy Lewallen wrote:
Comments interspersed. . .

Keith Dysart wrote:
[snip]
I take this to imply that you are not happy with the simple "like
charge
repels"?

That's right. Although it's a true statement, I haven't seen any
explanation of why it would cause waves to bounce off each other.

And Roger suggested the counter-example which may mark the end of
the line for "bounce".

[snip]
I would really appreciate seeing some other possible explanations.

How about this: During the initial turn-on of the system, energy does
cross the magic node. It's only in the theoretical limiting case of
steady state that the energy goes into and out of the node but doesn't
cross it. I'll argue that the limiting case can never be reached --
since this whole setup is a perfect construct to begin with. Or, if
that's not adequate by itself, what's the problem with energy being
trapped between nodes once the line is charged and steady state is reached?

I do use the view that the energy is trapped. The difficulty is: What
is the mechanism that traps the energy?

[snip]
With this explanation, P(t)
is definitely equal to V(t) time I(t), which I do appreciate.
The weakness of this explanation is that it seems to deny
that the wave moves energy. And yet before the pulses collide
it is easy to observe the energy moving in the line, and if
a pulse was not coming in the other direction, there would
be no dispute that the energy travelled to the end of the
line and was absorbed in the load. Yet when the pulses
collide, no energy crosses the middle of the line. Yet
energy can be observed travelling in the line before
and after the pulses collide.

I think the basic problem here is assigning energy to each traveling
wave.

I agree. And when looking at sinusoidal excitation with "standing
waves", it easy not to assign energy.

But when looking at pulses, the energy in the pulse seems to jump
out at me, and it is hard to ignore.

It's taking you into exactly the same morass that Cecil constantly
finds himself in.

I know. And I definitely do not want to go there.

And yet, when I look at pulses, where the energy is clearly visible,
I develop some sympathy for Cecil's position.

He also concluded some time back that two waves which
collide had to reverse direction in order to conserve power, energy,
momentum, or something. Energy in the system is conserved; but nowhere
is it written that each wave has to have individually conserved energy.

[snip]
I think you need to take a closer look at what it's getting you out
from. I believe the problem lies there.

Possibly.

[snip]
So I am not convinced that it any way goes against established theory.
I have not seen established theory attempt an explanation of how the
waves can both transport energy as well as not do so when waves of
equal energy collide.

Perhaps that's because individual waves don't transport energy that has
to be conserved?

Possibly, but the energy is so clearly visible in the pulses before
and
after they collide.

[snip]
The same concern that arises for pulses of equal voltage also
occurs for pulses of different voltage. While the mid-point no
longer has zero current, the actual current is only the difference
of the two currents in the pulses, the charge that crosses is only
the difference in the charge between the two pulses, and the
power at the mid-point is exactly the power that is needed
to move the difference in the energy of the two pulses.

Sorry, I'm having trouble following that. Voltage, current, charge, and
energy all in two sentences has too high a concept density for me to handle.

I'll try with a better description. Consider a line 4 sec long with
a matched pulse generator at each end. There is an instantaneous power
(p(t)=v(t)*i(t)) meter at the 1, 2 and 3 sec points on the line.
Call them the left, middle and right meters.
The left generator launches a 1 sec pulse of 100 volts and 2 amps (it
is
50 ohm line). This pulse is 200 W and contains 200 J.
Simultaneously the right generator launches a 1 sec pulse of 50 volts
and 1 amp (50 W and 50 J).
At 1 sec the left power meter reads 200 W for 1 sec as 200 J pass,
then at 3 sec the right power meter reads 200 W for 1 sec as 200 J
pass. It sure looks like the pulse has travelled down the line.
At 1 sec the right power meter reads -50 W for 1 sec as 50 J pass,
then at 3 sec the left power meter reads -50 W for 1 sec as 50 J
pass. It sure looks like this pulse has travelled up the line.
The total energy transfer measured by the left meter is 150 J and
by the right meter is also 150 J.
At second 2, when the pulses collide in the middle, the middle meter
reads 150 W for 1 second. So the total energy transfer at the middle
is 150 J, which is good since it agrees with the totals in the other
meters.

So the middle meter reads 150 W.
The left meter reads 200 W and later -50 W.
And the right meter reads -50 W and later 200 W.

So how does a pulse that measurably is 200 W (measured at both right
and left meters) move through a point that only measures 150 W.

Numerologically it surely does appear that one can superpose powers
since 200+(-50) is 150.

The main difference between this experiment and one with steady state
sinusoidal waves is that in the latter the component forward and
reverse waves in are derived by arithmetic from the actual conditions
on the line and it is easy to wave the issues away by saying that the
component waves have no reality. They are just intermediate results
in some arithmetic.

This waving away is much harder to do for the pulse case because
the pulses can be individually observed as actual conditions on the
line.

So the challenge is not so starkly obvious as it is when the
power at the mid-point is always 0, but P(t) = V(t) * I(t) can
still be computed and it will not be sufficient to allow
the energy in the two pulses to cross the mid-point (unless
one likes superposing power, in which case it will be
numerologically correct).

No, it'll have to be done without superposing power. Simple calculations
clearly show where the power is and where the energy is going, without
the need to superpose power or assign power or energy to individual waves.

Yes. And I find it easy to obscure for the sinusoid case. But the
pulses
seem to make it easy to measure and not so easy to refrain from
assigning
energy and power to the pulses.

[snip]
But if one conceives waves as also including energy, then it
seems that the question 'where does the energy go' is valid
and the common explanations do not seem to hold up well.

I think you're partially right about that. Partially, because I think
there's an underlying assumption that the power in an individual wave
has to be conserved. If you do insist on assigning energy to individual
traveling waves, I think you have to be willing to deal with the fact
that the energy can be swapped and shared among different waves, and
stored and returned as well.

But then, what is the mechanism that swaps the power between the
pulses
and changes the direction of the energy flow?

Our common analytical techniques deal with E and H fields which we can
superpose. In a transmission line, these are closely associated with
voltages and currents. They add nicely to make a total with properties
we can measure and characterize, and the total can neatly be created as
the sum of individual traveling waves from turn on until steady state.
It all works very well. Two fields, voltages or currents can easily add
to zero simply by being oriented in opposite directions -- and they do,
all along a transmission line. But how are the energies they supposedly
contain going to add to zero? You'll have to construct a whole new model
if you're going to require conservation of energy of individual
traveling waves.

I agree. And it especially will fail if instead of dealing with
the sum of the reflected waves, we try to sum the power of each
reflection
individually.

And yet, the power and energy are so visible when looking at pulses.

I'm absolutely certain that after all the work of
developing a self-consistent model with all interactions quantitatively
and mathematically explained and accounted for, we'll find a testable
case where some measurable result will be different from the
conventional viewpoint. (Google "ultraviolet catastrophe".) That would
then establish the validity of the new model. But I'm just as certain
that no such mathematical model will ever be forthcoming.

The advantage to the non-interacting traveling wave model
is that it so neatly predicts transient phenomena such as TDR and run-up
to steady state. I spent a number of years designing TDR circuitry,
interfacing with customers, and on several occasions developing and
teaching classes on TDR techniques, without ever encountering any
phenomena requiring explanations beyond classical traveling wave theory..
So you can understand my reluctance to embrace it based on a problem
with energy transfer across a single infinitesimal point in an ideal line.

Yes, indeed. Though any (new) explanation would have to remain
consistent with the existing body of knowledge which works so well.

Either that, or be able to demonstrate where the existing knowledge
fails. I'm not holding my breath.

I do not expect that to happen. But how is the energy in the left
travelling
50 W pulse turned around at the middle to add to the 150 W that is let
through
to complete the 200 W right travelling pulse?

...Keith

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
But at the points where the current or voltage is always
zero, it seems to me unnecessary to use the qualifier "*net*"
since the power IS always zero [from p(t)=v(t)*i(t)]. That
is, unless you are introducing another interpretation of
"*net*".

A standing wave is the *net* result of the superposition of
the forward wave and the reflected wave (without which the
standing wave would not exist). Anything, including power,
calculated using standing waves is necessarily a *net* result.
Superposed voltage is a net voltage. Superposed current is
a net current.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
I do use the view that the energy is trapped. The difficulty is: What
is the mechanism that traps the energy?

Photonic energy cannot be trapped in a homogeneous medium.
It is simply impossible to accomplish that feat without
any discontinuities to cause reflections.

The energy components are not trapped. There is exactly the
amount of energy in the line as required to support the
forward wave and reflected wave. The concept of trapped
energy is an illusion, an artificial shuffling of the
component energy. Modulation will reveal exactly
what is happening. I like TV ghosting examples.

Standing light waves can happen in free space. There is no
mechanism that traps the energy because there is no trapped
energy.

And yet, when I look at pulses, where the energy is clearly visible,
I develop some sympathy for Cecil's position.

He also concluded some time back that two waves which
collide had to reverse direction in order to conserve power, energy,
momentum, or something. Energy in the system is conserved; but nowhere
is it written that each wave has to have individually conserved energy.

For the record, what Roy said above is a false statement.
Canceled waves are necessarily moving in the same direction
at the same speed. It is impossible for them to collide.

Roy cannot produce even a single example where I said
colliding waves reverse direction in a homogeneous medium.

And it is certainly written that *all* energy, individual or
not, must be conserved. Not only must the energy in each
wave be conserved, the momentum in that wave must also
be conserved.

Numerologically it surely does appear that one can superpose powers
since 200+(-50) is 150.

Superposition requires a phase angle and power has no phase
angle so superposition cannot apply.

However, in the complete absence of interference, powers
can certainly be added. In the irradiance equation, if the
interference term is zero, the sum of two powers is simply
P1 + P2. It happens when the two waves are normal to each
other.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
The energy in
the canceled waves is "redistributed" in the opposite direction
in the transmission line as constructive interference.

But as I said, there is no energy where there are no waves, so the
sentence makes no sense. There is no "energy in canceled waves".

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
Cecil Moore wrote:
The energy in
the canceled waves is "redistributed" in the opposite direction
in the transmission line as constructive interference.

But as I said, there is no energy where there are no waves, so the
sentence makes no sense. There is no "energy in canceled waves".

There existed energy in the two waves before they were canceled.
Their ExH Poynting vectors had equal magnitudes and direction.
Their phases were opposite and they canceled. Their energy
components cannot be canceled or annihilated so the energy
is redistributed in the only other direction available. Exactly
what is it about the FSU web page that you do not understand?

Concerning the reflected wave cancellation process at a non-
reflective 1/4WL thin-film coating:

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are
180-degrees ... out of phase with each other meet, they are not
actually annihilated, ... All of the photon energy present in
these waves must somehow be recovered or redistributed in a new
direction, according to the law of energy conservation ... Instead,
upon meeting, the photons are redistributed to regions that permit
constructive interference, so the effect should be considered as
a redistribution of light waves and photon energy rather than
the spontaneous construction or destruction of light."

From Ramo & Whinnery, Page 440: Waveguides - Elimination
of Reflections from Dielectric Slabs.

"For slabs of any thickness, reflections may be eliminated
by canceling the reflected wave from one slab by that from
another placed a proper distance from it."

Before wave cancellation, the two waves contained energy.
After cancellation, they ceased to exist in their original
direction of travel. Energy cannot cease to exist so it
has to go somewhere. This is not rocket science.

You have tied yourself into a Gordian Knot. If there is
no canceled wave energy to redistribute, then there were
no reflected waves to begin with and the anti-reflective
coating was completely unnecessary. Peel it off and see
what happens.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Jim Kelley wrote:

Cecil Moore wrote:

The energy in
the canceled waves is "redistributed" in the opposite direction
in the transmission line as constructive interference.


But as I said, there is no energy where there are no waves, so the
sentence makes no sense. There is no "energy in canceled waves".


There existed energy in the two waves before they were canceled.

I really don't want to go on ad infinitum about this, but the only
"before" would have been "before" the conditions for wave cancellation
existed.

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:


Cecil Moore wrote:
There existed energy in the two waves before they were canceled.

I really don't want to go on ad infinitum about this, but the only
"before" would have been "before" the conditions for wave cancellation
existed.

Wave cancellation is a continuous steady-state process.
Every instant of present time, reflected waves are in
the process of being canceled. The power density equation,

Ptot = P1 + P2 + 2*SQRT(P1*P2)cos(A)

is a continuous steady-state process.

The s-parameter equation, b1 = s11*a1 + s12*a2, is a
continuous steady-state process. If you square both
sides of the equation you get the power density equation
above. IT IS A CONTINUOUS STEADY-STATE PROCESS that
spans the past, present, and future until the power
down transient state begins.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

"Jim Kelley" wrote in message
...


Cecil Moore wrote:

If an EM wave exists, it's
Poynting vector is ExM. The energy in that individual wave *must*
be conserved. If that energy is not conserved, the conservation
of energy principle is violated.

When a wave is canceled, there is no wave. Therefore there can be no
energy associated with that wave. If there is energy, then it must be
associated with a wave that is not canceled. Same thing is true when I
have candy. If it's not in my left hand, then it must be in my right
hand. It's all very profound.


but you can neither create nor destroy energy, so it can't just be
'canceled' it has to be either converted to some other form of energy or go
somewhere else... it can't just disappear.

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

Jim Kelley wrote:



Cecil Moore wrote:

There existed energy in the two waves before they were canceled.


I really don't want to go on ad infinitum about this, but the only
"before" would have been "before" the conditions for wave cancellation
existed.


Wave cancellation is a continuous steady-state process.
Every instant of present time, reflected waves are in
the process of being canceled.

During which time everything "before" is exactly the same as
everything "after".

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Keith Dysart wrote:
On Jan 15, 2:24 am, Roy Lewallen wrote:
The little program I wrote shows that, on the line being analyzed, the
energy is changing -- moving -- on both sides of a point of zero power.
Energy is flowing into that point from both directions at equal rates,
then flowing out at equal rates. This causes the energy at that point to
increase and decrease. What zero power at a given point means is that
there is no *net* energy moving in either direction past that point.

"*net* energy moving" seems to be a bit of a dangerous notion.

If "*net* energy moving" is the time averaged power, then
it is zero at *every* point on the line under consideration.
And I do not mind this definition.

That was probably a bad choice of words on my part. By net I didn't mean
an average over some period of time. I meant energy moving past a single
point.

One possibility I envisioned was some energy moving past the point from
left to right, and at the same time an equal amount moving at the same
rate past the point from right to left, resulting in zero power at the
point. However, on reflection, this couldn't happen; energy flows
"downhill". But the phenomenon observed on the open circuited line does
occur, where energy flows into the point from both directions equally,
and out of the point to both directions equally, resulting in zero power
at the point. No energy is flowing past the point, period -- the
modifier "net" isn't necessary.

But at the points where the current or voltage is always
zero, it seems to me unnecessary to use the qualifier "*net*"
since the power IS always zero [from p(t)=v(t)*i(t)]. That
is, unless you are introducing another interpretation of
"*net*".

You're right. Please consider "net" retracted.

Roy Lewallen, W7EL

Standing-Wave Current vs Traveling-Wave Current
 

Roy Lewallen wrote:
But the phenomenon observed on the open circuited line does
occur, where energy flows into the point from both directions equally,
and out of the point to both directions equally, resulting in zero power
at the point. No energy is flowing past the point, period --

Either energy flows past the point or else it is reflected.
Please provide an example of reflections occurring in a
homogeneous medium.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
During which time everything "before" is exactly the same as everything
"after".

Yes, we want the reflections to be continuously canceled
in real time and for the reflected energy to be redistributed
back toward the load in real time.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Dave wrote:
"Jim Kelley" wrote in message
...


Cecil Moore wrote:


If an EM wave exists, it's
Poynting vector is ExM. The energy in that individual wave *must*
be conserved. If that energy is not conserved, the conservation
of energy principle is violated.

When a wave is canceled, there is no wave. Therefore there can be no
energy associated with that wave. If there is energy, then it must be
associated with a wave that is not canceled. Same thing is true when I
have candy. If it's not in my left hand, then it must be in my right
hand. It's all very profound.



but you can neither create nor destroy energy, so it can't just be
'canceled' it has to be either converted to some other form of energy or go
somewhere else... it can't just disappear.

Hi Dave -

I think most people here are already quite aware of that. To what
energy do you specifically refer?

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
I think most people here are already quite aware of that. To what energy
do you specifically refer?

Probably the wave energy that you say never existed.
But you have never provided an example of waves
that can exist without energy.

Set the FSU flash example to 180 degrees out of
phase and please explain conceptually where the
energy in those two waves goes when they
superpose to zero in a transmission line.

http://micro.magnet.fsu.edu/primer/j...ons/index.html
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

Jim Kelley wrote:

I think most people here are already quite aware of that. To what
energy do you specifically refer?


Probably the wave energy that you say never existed.

So unless somebody can point to the energy that is "in" waves which
don't exist, then I will have to stick with the idea that there is no
energy to be associated with waves that don't exist. To me it is the
only logical way to look at it, even though I may be subject to abuse
from crackpots. ;-)

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

Jim Kelley wrote:

So unless somebody can point to the energy that is "in" waves which
don't exist, then I will have to stick with the idea that there is no
energy to be associated with waves that don't exist.


Jim, here is the s-parameter equation for the waves that
you assert don't exist.

b1 = s11*a1 + s12*a2 = 0

s11*a1 is not zero. s12*a2 is not zero. How you can assert
that they don't exist is really strange.

Perhaps I just understand the meaning of zero better than you do?

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
So unless somebody can point to the energy that is "in" waves which
don't exist, then I will have to stick with the idea that there is no
energy to be associated with waves that don't exist.

Jim, here is the s-parameter equation for the waves that
you assert don't exist.

b1 = s11*a1 + s12*a2 = 0

s11*a1 is not zero. s12*a2 is not zero. How you can assert
that they don't exist is really strange. Not only do they
exist but the HP apnote 95-1 even tells us that the power
associated with them is |s11*a1|^2 and |s12*a2|^2. You will
find that the powers obey the power density (irradiance)
equation from the field of optical physics.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
s11*a1 is not zero. s12*a2 is not zero. How you can assert
that they don't exist is really strange.

Perhaps I just understand the meaning of zero better than you do?

OTOH, perhaps not. If my bank balance is zero, does that
mean there have been zero debits and zero credits over
the entire previous month?
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:
Jim Kelley wrote:

s11*a1 is not zero. s12*a2 is not zero. How you can assert
that they don't exist is really strange.


Perhaps I just understand the meaning of zero better than you do?


OTOH, perhaps not. If my bank balance is zero, does that
mean there have been zero debits and zero credits over
the entire previous month?

Nope. Keep trying though. You'll get it if you really put your mind
to it.

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:

Cecil Moore wrote:
Jim Kelley wrote:
Perhaps I just understand the meaning of zero better than you do?

OTOH, perhaps not. If my bank balance is zero, does that
mean there have been zero debits and zero credits over
the entire previous month?

Nope. Keep trying though. You'll get it if you really put your mind to
it.

It is a gross confusion of cause and effect to say:
"If two waves superpose to zero, those two waves
don't exist." If the component waves being emitted
by a Yagi antenna don't exist, then it is a waste
of time and money to put up a Yagi antenna.

Maybe you should notify HP that they are wasting their
time publishing the following equation since s11*a1
and s12*a2 don't exist.

b1 = s11*a1 + s12*a2 = 0

That equation does *not* imply that s11*a1 and s12*a2
must equal zero. In fact those non-zero values are easy
to calculate. Square each and you have the power associated
with each of those components.

The irradiance equation from optical physics can be
derived by squaring the s-parameter normalized voltage
equation. Since (a1*a2) is a phasor term in that equation,
the phase angle between a1 and a2 must be included in the
result.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

On Jan 19, 5:04*am, Cecil Moore wrote:
It is a gross confusion of cause and effect to say:
"If two waves superpose to zero, those two waves
don't exist."

Then it should be a simple matter for you to actually measure the
canceled waves and their energy in order to prove everyone wrong once
and for all.

If the component waves being emitted
by a Yagi antenna don't exist, then it is a waste
of time and money to put up a Yagi antenna.

Maybe you should notify HP that they are wasting their
time publishing the following equation since s11*a1
and s12*a2 don't exist.

b1 = s11*a1 + s12*a2 = 0

That equation does *not* imply that s11*a1 and s12*a2
must equal zero. In fact those non-zero values are easy
to calculate. Square each and you have the power associated
with each of those components.

And yet when b1=0, they refuse to deliver any. It doesn't seem to
lend much support for your claim.

The irradiance equation from optical physics can be
derived by squaring the s-parameter normalized voltage
equation. Since (a1*a2) is a phasor term in that equation,
the phase angle between a1 and a2 must be included in the
result.
--
73, Cecil *http://www.w5dxp.com

None of the well proven methods shows a need for there to be any
energy in canceled, non-existant waves. HP would certainly never
affiliate themselves with a claim that there's energy associated with
waves that don't exist. The irradiance equation with all its "phasor
terms" is no help either. Where there is no irradiance, there is no
EM energy. Even Yagi antennas fail to radiate energy from their null
points. The only person I've ever seen claiming that there is energy
in non-existant waves is you, Cecil. On it's face, the idea is
ludicrous. And apparently you don't even find beauty in the fact that,
with no energy traveling in the direction of cancelled waves, there is
no need to invent a "4th mechanism of reflection" in order to conserve
that energy and get it moving in its correct direction of travel. As
a bonus, there is no need for religious beliefs that interference and
wave interaction cause waves to change direction. Accepting this
would of course mean yet another delay in the quest for martyrdom.

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

wrote:
Then it should be a simple matter for you to actually measure the
canceled waves and their energy in order to prove everyone wrong once
and for all.

The energy in the canceled waves is why the forward
power is often greater than the source power. As the
Melles-Groit web page says:

http://www.mellesgriot.com/products/optics/oc_2_1.htm

"Clearly, if the wavelength of the incident light and the
thickness of the film are such that a phase difference exists
between reflections of p, then reflected wavefronts interfere
destructively, and overall reflected intensity is a minimum.
If the two reflections are of equal amplitude, then this
amplitude (and hence intensity) minimum will be zero."

When it is zero, total destructive interference and wave
cancellation has occurred.

"In the absence of absorption or scatter, the principle of
conservation of energy indicates all 'lost' reflected intensity
will appear as enhanced intensity in the transmitted beam. The
sum of the reflected and transmitted beam intensities is always
equal to the incident intensity. THIS IMPORTANT FACT HAS BEEN
CONFIRMED EXPERIMENTALLY." (emphasis mine)

Melles-Groit says it has been confirmed experimentally.
That's good enough for me. What it is about the Melles-Groit
web page that you don't understand?

And yet when b1=0, they refuse to deliver any.

No, the the energy is delivered (redistributed) in the
opposite direction. What is it about the FSU web page
that you don't understand?

http://micro.magnet.fsu.edu/primer/j...ons/index.html

"... when two waves of equal amplitude and wavelength that are
180-degrees ... out of phase with each other meet, they are not
actually annihilated, ... All of the photon energy present in
these waves must somehow be recovered or redistributed in a new
direction, according to the law of energy conservation ... Instead,
upon meeting, the photons are redistributed to regions that permit
constructive interference, so the effect should be considered as
a redistribution of light waves and photon energy rather than
the spontaneous construction or destruction of light."

None of the well proven methods shows a need for there to be any
energy in canceled, non-existant waves.

The Melles-Groit web page says the energy in the canceled waves
"appears as enhanced intensity in the transmitted beam" (forward wave).

The FSU web page says the energy in the canceled waves is
"redistributed to regions that permit constructive interference"
(forward wave).

That's good enough for me.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

wrote:

Then it should be a simple matter for you to actually measure the
canceled waves and their energy in order to prove everyone wrong once
and for all.


The energy in the canceled waves is why the forward
power is often greater than the source power.

But that's in the wrong direction, Cecil. You claim there's power in
the canceled waves. You need to be able to measure that for the proof
of your belief. Obviously there's energy in the forward waves.
They're not canceled.

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
You claim there's power in the canceled waves.

That is a false statement and you are either totally
confused or bearing your usual false witness.
I have never claimed that there is power in the
canceled waves *after* they cancel, only that there
was energy in them *before* cancellation took place.
The HP ApNote 95-1 on s-parameters agrees with me.

b1 = s11*a1 + s12*a2 now square both sides

|b1|^2 is the reflected power
|s11|^2 is the power reflection coefficient
|a1|^2 is the forward power
|s12|^2 is the power transmission coefficient
|a2|^2 is the reflected power

It's obvious that you don't understand the HP
ApNote.

There's zero energy in the total superposed wave
after cancellation. There was energy in the two
waves before they were superposed. That energy
cannot be destroyed no matter how loudly you complain.
It is more than apparent that you detest the conservation
of energy principle because it works against your
argument. But as they say in Russia, tough ****sky.

When two waves are canceled, their energy components
are redistributed to another area. In a transmission
line, with only two directions possible, their energy
components are redistributed in the other direction
from their original direction of flow. What is it about
the Melles Groit and FSU web pages that you don't
understand and what is it about the following that you
don't understand?

"The waves' energies simply add together. In places where
the interference is destructive, one wave cancels out the
other. (up + down = nothing.) Where it is constructive,
however, they reinforce each other
(up + up = 2 * up, down + down = 2 * down.)
That is all there is to it."

Richard E. Barrans Jr., Ph.D.
Assistant Director
PG Research Foundation, Darien, Illinois

P3 + P4 - 2*SQRT(P3*P4) = 0 = nothing
P1 + P2 + 2*SQRT(P1*P2) = 2P1 + 2P2
That is all there is to it.
--
73, Cecil http://www.w5dxp.com

Standing-Wave Current vs Traveling-Wave Current
 

Cecil Moore wrote:

wrote:

Then it should be a simple matter for you to actually measure the
canceled waves and their energy in order to prove everyone wrong once
and for all.



The energy in the canceled waves is why the forward
power is often greater than the source power.

But that's in the wrong direction, Cecil. You claim there's energy in
the canceled waves. You need to be able to measure that for the proof
of your belief. Obviously there's energy in the forward waves. They're
not canceled.

ac6xg

Standing-Wave Current vs Traveling-Wave Current
 

Jim Kelley wrote:
Cecil Moore wrote:
The energy in the canceled waves is why the forward
power is often greater than the source power.

But that's in the wrong direction, Cecil. You claim there's energy in
the canceled waves. You need to be able to measure that for the proof
of your belief. Obviously there's energy in the forward waves. They're
not canceled.

I certainly do *NOT* claim there's energy in the
canceled waves after they are canceled. If you could
win the argument without bearing false witness, you
would already have done so.

You seem to be acting obtuse just for the hell of it.
There is energy in the canceled waves before they are
canceled. It's equal to 2*ExB. After they are canceled,
that 2*ExB energy heads in the opposite direction toward
the load. Consider that the following s-parameter
equation is a steady-state process.

b1 = s11*a1 + s12*a2 = 0

This is a continuous steady-state process. There is
energy in s11*a1. The power is equal to |s11*a1|^2
because s11 and a1 are not zero. There is energy in
s12*a2. The power is equal to |s12*a2|^2 because s12
and a2 are not zero. The power in b1 is equal to |b1|^2.

|s11*a1|^2 + |s12*a2|^2 - destructive interference = 0

For instance,

|s11*a1|^2 = 100 watts, |s12*a2| = 100 watts

Is that calculation beyond your math capabilities?

100w + 100w + 2*SQRT(100w*100w) = 0

There is a total of 200 watts in the two waves just
before they cancel during steady-state. Those 200 watts
head back toward the load after they cancel. That is
*NOT* a one time occurrence. It is a continuous steady-
state occurrence. The two waves are being continuously
canceled during a steady-state wave cancellation process.

Please read the HP ApNote 95-1 until you understand it.
Please study the irradiance equation until you understand
that it is a steady-state process.
--
73, Cecil http://www.w5dxp.com