Tom Donaly wrote:
you come up with the right answer, but is your
interpretation correct? Can you do the same thing in a
general sense? If there is no Z0 match between the two
transmission lines, does your method still work?

As a stand alone analysis, it yields two possible solutions
but the purpose of this discussion is not to come up with
a new stand alone method of analysis. The purpose is, given
a standard analysis, to add TRACKING OF THE ENERGY COMPONENTS
through an impedance discontinuity, something many people
believe to be impossible.

It wasn't designed to work as a stand alone analysis but
it does for Z0-matched systems, the most usual ham
configuration. However, an additional piece of information
is required in the general case to be able to tell which
voltage is leading and which is lagging.

(P.S. The method of using V and I and the junction of
the two xmission lines to find the forward and reverse
powers on a transmission line doesn't prove the powers exist.

Do you think the powers defined in HP App Note 95-1 exist?
Remember my one second long transmission line example where
the number of stored joules exactly equaled the number of joules
required by the forward wave and the reflected wave? If the
energy is not in those waves, where is it? Nobody has
provided any explaination of how standing waves can exist
without forward and reflected waves. Under "standing wave",
The IEEE Dictionary says: "A pure standing wave results
from the interference of two oppositely directed traveling
waves of the same frequency and amplitude." i.e. standing
waves are the result (effect), two oppositely directed
traveling waves are the *cause*. Most of my references
agree. The forward and reflected wave energy components
must exist as causes before standing waves can materialize
as an effect.
--
73, Cecil http://www.qsl.net/w5dxp


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Cecil Moore wrote:

Who said powers can never be added?

Must have been someone who was unfamiliar with the expression 'figures
can lie and liars can figure'.
:-)

ac6xg

Jim Kelley wrote:

Cecil Moore wrote:
Who said powers can never be added?

Must have been someone who was unfamiliar with the expression 'figures
can lie and liars can figure'. :-)

You reckon Eugene Hecht was lying when he shows us how to
add two irradiances to obtain the total irradiance (power
per unit-area) in _Optics_? Adding EM wave powers during
interference is a well accepted way of handling EM wave
superposition in the field of optics. The bright constructive
interference rings contain more power than the dark destructive
interference rings. RF waves and light waves are both electro-
magnetic waves, just at different frequencies. Asserting that
RF waves obey a different set of laws of physics than do light
waves is naive ignorance at best.
--
73, Cecil http://www.qsl.net/w5dxp

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Cecil Moore wrote:

Jim Kelley wrote:

Cecil Moore wrote:

Who said powers can never be added?


Must have been someone who was unfamiliar with the expression 'figures
can lie and liars can figure'. :-)


You reckon Eugene Hecht was lying when he shows us how to
add two irradiances to obtain the total irradiance (power
per unit-area) in _Optics_?

Eugene Hecht doesn't have a dog in this fight, Cecil. But the quote is
a truism that applies in any case. Wrong numbers added correctly
produce a wrong number; correct numbers added incorrectly produce an
incorrect number; and in the special case, certain wrong numbers added
in a particular incorrect way can produce a desired result.

You take too great a liberty with the name Eugene Hecht. Among the
things which won't be found in any of Dr. Hecht's texts is a minus sign
in front of number expressing an irradiance. Nor will we find a
negative scalar quantity accompanied by the claim that the negative sign
indicates a change in direction, as you have done. Eugene Hecht also
did not claim that interference could be a cause for energy to reflect
or otherwise change direction, as you have done. Such claims are
blatently false.

Power and irradiance are derived and dependent quantities, not
fundamental independent quantities in nature. And although an
automobile moves at some speed, the scaler quantity itself is not
something which moves. Similarly, power and irradiance do not
physically propagate and they do not physically interact. 'They' do not
reflect, refract, diffract, disperse, interfere, or act upon other
'powers' or 'irradiances'. JC Maxwell and others observed that it is
electric and magnetic fields which propagate, interact with matter, and
add algebraically and vectorially. When fields physically interact with
matter, we can measure their effect and can quantify such things as
voltage, current, and heat, and hence calculate such things as power or
irradiance. But it is actually the fields themselves which
algebraically sum. Of course the interference equation accurately
expresses power and irradiance. The fact that power and irradiance
generally go as the square of the fields allows us to correctly make
certain additional mathematical assumptions. One must still be careful
not to mistake an effect for a cause. But it is the 2nd Amendment, the
internet, and the absence of peer review which afford men the freedom
and means to work equations and describe physical phenomena in any way
they like.

73, ac6xg

Jim Kelley wrote:

Jim, you have a habit of erecting strawmen somewhat like:
"I don't care what you say, the sun will rise tomorrow." For that
reason, I'm going to trim the parts of your posting with which I
agree and have never disagreed.

You take too great a liberty with the name Eugene Hecht. Among the
things which won't be found in any of Dr. Hecht's texts is a minus sign
in front of number expressing an irradiance.

Sure wish you would read the book before making such statements.

On the contrary, here's equation (9.16) representing total destructive
interference.

Imin = I1 + I2 - 2*SQRT(I1*I2) = 0

The third term is indeed a minus sign in front of a number expressing
irradiance. However, total average irradiance cannot be less than zero.
And for the record, I have never said total average power could be less
than zero but, like Hecht, I treat destructive interference energy as a
negative term and constructive interference energy as a positive term.

Dr. Stephen Best, VE9SRB, did the same thing for his "Wave Mechanics
of Transmission Lines, Part 3:" QEX article, Nov/Dec 2001. He said:

"When the voltages V1 and V2 are exactly 180 deg out of phase, the
total power can be determined as follows:"

"PFtotal = P1 + P2 - 2*SQRT(P1)*SQRT(P2)"

so if you don't like negative power terms, you should confront both
Eugene Hecht and Dr. Best.

Nor will we find a
negative scalar quantity accompanied by the claim that the negative sign
indicates a change in direction, as you have done.

On the contrary, in equation 9.16 above, according to Hecht, the
interference term is negative indicating "total destructive
interference", his words, not mine. Here's Hecht's quote from _Optics_.

“The principle of
conservation of energy makes it clear that if there is constructive
interference at one point, the ‘extra’ energy at that location must have
come from somewhere else. There must therefore be destructive
interference somewhere else."

Sorry, but a negative interference term denotes destructive
interference. A positive interference term denotes constructive
interference. In a transmission line with only two directions,
if destructive interference occurs in one direction, then
constructive interference must occur in the only other direction
in order to satisfy the conservation of energy principle.

A wave cancellation event in a transmission line implies an equal
constructive interference event in the opposite direction. Anything
else violates the laws of physics.

Similarly, power and irradiance do not
physically propagate and they do not physically interact.

On the contrary, they do physically interact for coherent waves as can
be inferred by the interference equations. Please reference Chapter 9
in _Optics_, by Hecht. The mathematical interaction of power and
irradiance is a *result* of superposition of coherent EM waves. That's
where the interference equations involving irradiance come from.

JC Maxwell and others observed that it is
electric and magnetic fields which propagate, interact with matter, and
add algebraically and vectorially.

And contain power equal to ExH. EM waves cannot exist without energy.
If EM waves interact, their energy components interact. Destructive
and constructive interference cannot occur without energy components
which follow the laws of physics.

Of course the interference equation accurately expresses power and
irradiance.

That is some progress on your part so there's hope. What you need to
realize is that those interference equations define what happens to
the energy at a match point in a transmission line. Dr. Best kicked
this discussion off by his QEX article. He just didn't realize that
the equations he published were virtually identical to the classical
optical interference equations.
--
73, Cecil http://www.qsl.net/w5dxp


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On Tue, 12 Jul 2005 22:48:00 -0500, Cecil Moore
wrote:

Nor will we find a
negative scalar quantity accompanied by the claim that the negative sign
indicates a change in direction, as you have done.

On the contrary, in equation 9.16 above, according to Hecht, the
interference term is negative indicating "total destructive
interference", his words, not mine. Here's Hecht's quote from _Optics_.

[Hecht rolls his eyes] Jim's point is won, absolutely nothing quoted
here explicitly states a change in direction. That is, as Jim points
out, the math follows the physics, it does not create the physics.
There is a vast gulf between being descriptive and being proscriptive.

Richard Clark wrote:
[Hecht rolls his eyes]

I'm going to trim and ignore the condescending ad hominem stuff.

... the math follows the physics, it does not create the physics.

Your argument has that exact flaw. "What Cecil is describing doesn't
exist in the common math model. Therefore, the math model prohibits
it from existing in physics." Please follow your own advice. There
is a vast gulf between being descriptive and being prohibitive.

There is a vast gulf between being descriptive and being proscriptive.

I didn't choose to quote the entire book, Richard. Hecht also says:
"If two or more electromagnetic waves arrive at point P out-of-phase
and cancel, 'What does that mean as far as their energy is concerned?'
Energy can be distributed, but it doesn’t cancel out. ... The
superposition of coherent waves generally has the effect of altering
the spatial distribution of the energy but not the total amount
(of energy) present."

"Altering the spatial distribution of the energy" in a transmission
line is a binary function since there are only two directions. If
the spatial distribution is altered, it necessarily changes directions.

The following does explicitly state a change in direction, i.e. "A
NEW DIRECTION".

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." (Emphasis mine.)

A transmission line has only two directions. If wave cancellation, i.e.
permanent destructive interference, takes place in one direction, the
necessary corresponding constructive interference must be "redistributed
in a new direction". In a transmission line, there is only one "new
direction", the opposite direction from the old direction.
--
73, Cecil http://www.qsl.net/w5dxp

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On Wed, 13 Jul 2005 07:28:21 -0500, Cecil Moore
wrote:
There is a vast gulf between being descriptive and being proscriptive.
I didn't choose to quote the entire book
[Hecht rolls his eyes] That would have been futile because no portion
of it contains the proscription.

What has been offered makes as much sense as ascribing the value of
$100 to a button simply because you sewed it to a jacket and found
$100 in the pocket of that jacket. -Superstition-

Cecil Moore wrote:

"PFtotal = P1 + P2 - 2*SQRT(P1)*SQRT(P2)"

so if you don't like negative power terms, you should confront both
Eugene Hecht and Dr. Best.

Don't be foolish. Obviously neither of the P terms can be negative if
PFtotal is supposed to represent a real number. I have no issues to
confront with either of the gentlemen. It is where you diverge from
Hecht (and Maxwell, and Born and Wolfe, and Jackson) that I take issue.

Nor will we find a negative scalar quantity accompanied by the claim
that the negative sign indicates a change in direction, as you have done.


On the contrary, in equation 9.16 above, according to Hecht, the
interference term is negative indicating "total destructive
interference", his words, not mine. Here's Hecht's quote from _Optics_.

One statement does not contradict the other, as the subject in each
sentence is entirely different. Both statements are obviously true.

Similarly, power and irradiance do not physically propagate and they
do not physically interact.


On the contrary, they do physically interact for coherent waves as can
be inferred by the interference equations. Please reference Chapter 9
in _Optics_, by Hecht. The mathematical interaction of power and
irradiance is a *result* of superposition of coherent EM waves. That's
where the interference equations involving irradiance come from.

As I explained they come from the fact that the fields interact, and
that power and intensity (or irradiance) go as the square of the field.
Lets say the square of F1 (field 1) is proportional with P1, and the
square of F2 is proportional with P2. And lets say the mathematical
description of the way the two fields interact is as follows:
Ftotal = (F1 - F2)*(F1 - F2). (Looks kinda like modulation, but I
digress.) We can then write that as
Ftotal = F1^2 + F2^2 - 2*F1*F2. By substitution then,
PFtotal = P1 + P2 - 2*SQRT(P1*P2). And that's where your favorite
equation comes from.

73, ac6xg

Jim Kelley wrote:
It is where you diverge from
Hecht (and Maxwell, and Born and Wolfe, and Jackson) that I take issue.

I don't diverge from them, Jim. I have simply tied a few loose
ends together using logical deduction based on the laws of physics.
So far, you have produced zero instances where I diverge from
the laws of physics. OTOH, you appear to have diverged quite often,
e.g. Maxwell's equations prove that standing waves can exist without
a rearward-traveling wave, cancelled waves don't contain energy or
momentum before they are cancelled, reflected waves are not re-
reflected by wave cancellation, there is no before and after, etc.

PFtotal = P1 + P2 - 2*SQRT(P1*P2). And that's where your favorite
equation comes from.

I have said all along that energy cannot be separated from the waves
containing the energy and that's why an energy analysis is possible.
--
73, Cecil http://www.qsl.net/w5dxp


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