Roger Sparks wrote:
How can we justify calling the +/- 2*SQRT[Pf.g(t)*Pr.g(t) term the "interference term"?

Page 388, "Optics", by Eugene Hecht, 4th edition:
"The interference term becomes I12 = 2*SQRT(I1*I2)cos(A)"
where 'I' is the Irradiance (power density)[NOT Current]
Later Hecht says +2*SQRT(I1*I2) is the total constructive
interference term and -2*SQRT(I1*I2) is the total
destructive interference term. Chapter 9 is titled
"Interference" - recommended reading.

Am I correct in assuming that this equation describes the instantaneous power delivered to Rs?

Yes, if Tom, K7ITM, is correct about the equation working
for instantaneous power densities, not just for average
power densities as I had first assumed.

Let's say the instantaneous forward voltage dropped across
the source resistor is +50 volts and the instantaneous
reflected voltage across the source resistor is -30 volts.
The source resistor is 50 ohms.
Pf.rs(t) = (+50v)^2/50 = 50w
Pr.rs(t) = (-30v)^2/50 = 18w
Prs(t) = Pf.rs(t) + Pr.rs(t) - interference
Prs(t) = 50w + 18w - 2*SQRT(50*18) = 8 watts

If Tom is correct, that should be the actual dissipation
in the source resistor at that time which includes 60 watts
of destructive interference that will be dissipated 90 degrees
later when 2*SQRT(50*18) = +60 watts.
--
73, Cecil http://www.w5dxp.com

On Sun, 23 Mar 2008 09:03:31 -0500
Cecil Moore wrote:

Roger Sparks wrote:
How can we justify calling the +/- 2*SQRT[Pf.g(t)*Pr.g(t) term the "interference term"?

Page 388, "Optics", by Eugene Hecht, 4th edition:
"The interference term becomes I12 = 2*SQRT(I1*I2)cos(A)"
where 'I' is the Irradiance (power density)[NOT Current]
Later Hecht says +2*SQRT(I1*I2) is the total constructive
interference term and -2*SQRT(I1*I2) is the total
destructive interference term. Chapter 9 is titled
"Interference" - recommended reading.

Am I correct in assuming that this equation describes the instantaneous power delivered to Rs?

Yes, if Tom, K7ITM, is correct about the equation working
for instantaneous power densities, not just for average
power densities as I had first assumed.

Let's say the instantaneous forward voltage dropped across
the source resistor is +50 volts and the instantaneous
reflected voltage across the source resistor is -30 volts.
The source resistor is 50 ohms.
Pf.rs(t) = (+50v)^2/50 = 50w
Pr.rs(t) = (-30v)^2/50 = 18w
Prs(t) = Pf.rs(t) + Pr.rs(t) - interference
Prs(t) = 50w + 18w - 2*SQRT(50*18) = 8 watts

If Tom is correct, that should be the actual dissipation
in the source resistor at that time which includes 60 watts
of destructive interference that will be dissipated 90 degrees
later when 2*SQRT(50*18) = +60 watts.
--
73, Cecil http://www.w5dxp.com

Thanks for your thoughtful reply.

TanH(30/50) = 30.96 degrees. This takes us back to the 12.5 ohm load example.

Is it possible that in your example here, the reflected voltage acts in series with Rs but arrives 90 degrees out of phase with the forward voltage? If so, then

Vrs = sqrt(50^2 + 30^2) (the reflected voltage should ADD to the source voltage)

= sqrt(3400) = 58.31v

The power to Rs would be

Prs = (V^2)/50 = 3400/50 = 68w

We previously found that 32w was used at the 12.5 ohm load, so 32 + 68 = 100w. The entire output from the source is accounted for.

If this is the case, we have here an example of constructive interference, and complete accounting for the power.

You might wonder why I would consider this alternative. If the destructive interference included a 90 degree delay, how would I know whether the 30v was the delayed voltage or exactly in phase with the source? It must be delayed by 90 degrees because the forward voltage is always 90 degrees ahead of the reflected wave (in 45 degree line length example).

Your example certainly works as written, but it also introduces a dilemma. Where is the power stored for 90 degrees?

To answer that question, I see two possiblities: The source voltage causes a reflection so the 60w is stored as an additional reflected wave on the transmission line.

Or second, the 60w is stored in the source.

--
73, Roger, W7WKB

Roger Sparks wrote:
(the reflected voltage should ADD to the source voltage)

If you graph the two voltages you will find that half the time
the reflected voltage adds to the source voltage and half the
time the reflected voltage subtracts from the source voltage.
Both are true half the time. You can point out either case on
the graph. That's why the average interference term is zero
for this special case and therefore why 100% of the average
reflected power is dissipated in the source resistor for
this special case.

You might wonder why I would consider this alternative.
If the destructive interference included a 90 degree delay,
how would I know whether the 30v was the delayed voltage or
exactly in phase with the source?

By looking at the graphs?

Where is the power stored for 90 degrees?

In the equivalent reactance of the transmission line.

That's what reactances do in AC circuits. They store
energy and deliver it back to the system some time
later.
--
73, Cecil http://www.w5dxp.com

On Sun, 23 Mar 2008 19:57:24 GMT
Cecil Moore wrote:

Roger Sparks wrote:
(the reflected voltage should ADD to the source voltage)

If you graph the two voltages you will find that half the time
the reflected voltage adds to the source voltage and half the
time the reflected voltage subtracts from the source voltage.
Both are true half the time. You can point out either case on
the graph. That's why the average interference term is zero
for this special case and therefore why 100% of the average
reflected power is dissipated in the source resistor for
this special case.

You might wonder why I would consider this alternative.
If the destructive interference included a 90 degree delay,
how would I know whether the 30v was the delayed voltage or
exactly in phase with the source?

By looking at the graphs?

Where is the power stored for 90 degrees?

In the equivalent reactance of the transmission line.

That's what reactances do in AC circuits. They store
energy and deliver it back to the system some time
later.
--
73, Cecil http://www.w5dxp.com

I did not use a graph, but created a spreadsheet that calculated Vrs for the short circuit, 45 degree long line. It shows the 90 degree transfer of power that you described. I posted the spreadsheet in PDF format at http://www.fairpoint.net/~rsparks/Reflect_short.pdf.

To me, this shows that my traveling wave analysis on an instant basis is not correct because the energy can not be located precisely on a degree-by-degree scale. Yes, it is correct on the average over 360 degrees, but not instantaneously. We are missing something.

Central to traveling waves is the assumption that the wave is not compressable. The energy is assumed to flow in a consistantly predictable mannor that is linear and described by a sine wave. That assumption is violated when energy is delayed for reasons other than distance of travel, which is demonstrated in this example.

I am not ready to suggest a cure for my traveling wave analysis. I only see that it does not work to my expectations.

Thanks for providing the examples and comments.
--
73, Roger, W7WKB

Roger Sparks wrote:
To me, this shows that my traveling wave analysis on an instant basis
is not correct because the energy can not be located precisely on a
degree-by-degree scale. Yes, it is correct on the average over 360
degrees, but not instantaneously. We are missing something.

What you are missing is the localized interference patterns
within the individual cycles. The interference changes from
destructive to constructive every 90 degrees. For every
negative (destructive) interference term, there is an equal
magnitude positive (constructive) interference term 90 degrees
later. These, of course, average out to zero. Exactly the
same thing happens when a coil or capacitor is present in
a circuit. When the instantaneous voltage of a source is
zero and thus delivering zero instantaneous power, a
circuit capacitor is delivering energy back into the
circuit that can be dissipated by a resistor.

Central to traveling waves is the assumption that the wave is not
compressable. The energy is assumed to flow in a consistantly
predictable mannor that is linear and described by a sine wave.
That assumption is violated when energy is delayed for reasons
other than distance of travel, which is demonstrated in this example.

Power is certainly compressible. One can stuff 100 amphere-
hours into a battery in 2 hours and take 20 hours to remove it.
Why can't 60 watts of instantaneous power be stuffed into
a reactance and be removed 90 degrees later?

I am not ready to suggest a cure for my traveling wave analysis. I
only see that it does not work to my expectations.

Your expectations seem to be based on a conservation of
power principle which doesn't exist. There is no violation
of linearity if the energy dissipation is delayed by 90
degrees or by ten billion years.

I don't recall any published material where anyone tried
to explain where the instantaneous energy goes while at
the same time denying the possibility of interference.
--
73, Cecil http://www.w5dxp.com

On Mon, 24 Mar 2008 16:15:21 GMT
Cecil Moore wrote:

Roger Sparks wrote:
To me, this shows that my traveling wave analysis on an instant basis
is not correct because the energy can not be located precisely on a
degree-by-degree scale. Yes, it is correct on the average over 360
degrees, but not instantaneously. We are missing something.

What you are missing is the localized interference patterns
within the individual cycles. The interference changes from
destructive to constructive every 90 degrees. For every
negative (destructive) interference term, there is an equal
magnitude positive (constructive) interference term 90 degrees
later. These, of course, average out to zero. Exactly the
same thing happens when a coil or capacitor is present in
a circuit. When the instantaneous voltage of a source is
zero and thus delivering zero instantaneous power, a
circuit capacitor is delivering energy back into the
circuit that can be dissipated by a resistor.

Central to traveling waves is the assumption that the wave is not
compressable. The energy is assumed to flow in a consistantly
predictable mannor that is linear and described by a sine wave.
That assumption is violated when energy is delayed for reasons
other than distance of travel, which is demonstrated in this example.

Power is certainly compressible. One can stuff 100 amphere-
hours into a battery in 2 hours and take 20 hours to remove it.
Why can't 60 watts of instantaneous power be stuffed into
a reactance and be removed 90 degrees later?

I am not ready to suggest a cure for my traveling wave analysis. I
only see that it does not work to my expectations.

Your expectations seem to be based on a conservation of
power principle which doesn't exist. There is no violation
of linearity if the energy dissipation is delayed by 90
degrees or by ten billion years.

I don't recall any published material where anyone tried
to explain where the instantaneous energy goes while at
the same time denying the possibility of interference.
--
73, Cecil http://www.w5dxp.com

Hi Cecil,

I feel better today. I think I have connected the dots and now have the spreadsheet showing that we really can use the traveling waves to solve the shorted transmission line problem on a instantaneous basis without the delay of energy into the next half cycle.

Here is a link to the new spreadsheet.

http://www.fairpoint.net/~rsparks/Sm...Reflection.pdf

I used the logic and formula presented in my post "Subject: The Rest of the Story
Date: Thu, 20 Mar 2008 10:07:44 -0700"

You called it interference. Keith used your power equation and called the interference term a mathematical correction. It looks to me like the correction can be avoided by choosing the correct sin wave offset.

Ultimately, the waves can be resolved into one more powerful wave carrying the power described by Keith's "false power" equation. This is demonstrated in a spreadsheet found at

http://www.fairpoint.net/~rsparks/Re...em%20Power.pdf

You need to take a look at the spreadsheets. I think they support the theory that we can track the power on an instant basis using traveling waves.
--
73, Roger, W7WKB

Roger Sparks wrote:
You need to take a look at the spreadsheets.

Roger, in a nutshell, what is the bottom line?
--
73, Cecil http://www.w5dxp.com