Is the Superposition Principle invalid?
 

On Mar 30, 9:40 pm, Cecil Moore wrote:
Here is the way one sums the power in two energy waves. This
is one of the things that Dr. Best, ve9srb, got right in
his Nov/Dec 2001 QEX article, "Wave Mechanics of Transmission
Lines, Part 3: Power Delivery and Impedance Matching". This
article is what got me to thinking along my present lines.

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

Curiosity question: Which of the two possible values for
the square root did you use? Elaborate on the reasons
for your choice?

....Keith

Is the Superposition Principle invalid?
 

On Mar 30, 8:54 pm, Cecil Moore wrote:
Gene Fuller wrote:
Even if you could separate
the forward and reverse waves the Poynting vector energy calculation
would still come out to exactly zero for each component as well as the
sum of the components.

Forward and reflected waves are easily separated by a
circulator so their existence is difficult to deny.

You always seem to like changing the experiment and then not
acting surprised when you get different results.

Odd is it not?

....Keith

Is the Superposition Principle invalid?
 

Keith Dysart wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

Curiosity question: Which of the two possible values for
the square root did you use? Elaborate on the reasons
for your choice?

Probably should be written 2*|SQRT(P1*P2)|*cos(A) to
satisfy the purists. The sign of the interference
term must match the type of interference which is
determined by the sign of cos(A).

The third term in the equation is the interference term.
A positive value indicates constructive interference.
A negative value indicates destructive interference.
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

Keith Dysart wrote:
Cecil Moore wrote:
Gene Fuller wrote:
Even if you could separate
the forward and reverse waves the Poynting vector energy calculation
would still come out to exactly zero for each component as well as the
sum of the components.

Forward and reflected waves are easily separated by a
circulator so their existence is difficult to deny.

You always seem to like changing the experiment and then not
acting surprised when you get different results.

I don't see an experiment described in Gene's posting
so you must be describing yet another dream of yours.
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

On Mar 30, 10:04 pm, Cecil Moore wrote:
Keith Dysart wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)cos(A)

Curiosity question: Which of the two possible values for
the square root did you use? Elaborate on the reasons
for your choice?

Probably should be written 2*|SQRT(P1*P2)|*cos(A) to
satisfy the purists. The sign of the interference
term must match the type of interference which is
determined by the sign of cos(A).

More curiousity: Can P1 and P2 have different signs, that is,
the power is going in different directions? If so, how does the
resulting complex SQRT work into the result?

....Keith

Is the Superposition Principle invalid?
 

Keith Dysart wrote:
More curiousity: Can P1 and P2 have different signs, that is,
the power is going in different directions?

Please reference Chapter 9, Interference, in "Optics",
by Hecht, 4th edition. The two interfering waves are
traveling in the same direction. The associated
powers exist together at a point of interference.
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

Owen Duffy wrote in
:

....
Hecht's, it is your partical quote and elaboration) that states that

How did that 'c' get in there? Should have been:

Hecht's, it is your partial quote and elaboration) that states that

Is the Superposition Principle invalid?
 

On Sat, 31 Mar 2007 03:35:47 GMT, Cecil Moore
wrote:

Keith Dysart wrote:
More curiousity: Can P1 and P2 have different signs, that is,
the power is going in different directions?

Please reference Chapter 9, Interference, in "Optics",
by Hecht, 4th edition. The two interfering waves are
traveling in the same direction. The associated
powers exist together at a point of interference.

It's a shame you have only one reference that is so impoverished as to
restrict itself to this "same direction." Otherwise, you would have
been able to answer Keith's question without asking him to figure out
what you couldn't. It is, after all, a commonplace of superposition
(that is what this thread is about, isn't it?) - or are you the
doubting Thomas this thread's subject alludes to?

The stumbling over absolute values was funny too. I was wondering who
was going to pull that rug.

Is the Superposition Principle invalid?
 

On Mar 30, 11:35 pm, Cecil Moore wrote:
Keith Dysart wrote:
More curiousity: Can P1 and P2 have different signs, that is,
the power is going in different directions?

Please reference Chapter 9, Interference, in "Optics",
by Hecht, 4th edition. The two interfering waves are
traveling in the same direction. The associated
powers exist together at a point of interference.

This is getting way too confusing. After adding absolute value
to clarify which of two possible roots is being used (though
without any rigorous rationale), it turns out that different
formulae are needed depending on the direction.

So some times
Ptot = Pf - Pr
while at other times
Ptot = P1 + P2 + Pfudge

Are there other conditions we need to be aware of when computing
Ptot?

How does this align with your previous quote?
"Known as the *Principle of Superposition*, this property
suggests that the resultant disturbance at any point in a
medium is the algebraic sum of the separate constituent
waves."

Neither of the equations is the "algebraic sum".

....Keith

How does this align with your

Is the Superposition Principle invalid?
 

"Cecil Moore" wrote in message
...
Keith Dysart wrote:
Superposition of voltages and currents seems to be quite
accepted and is an excellent tool for circuit and transmission
line analysis.

Do you really expect us to believe that those voltages
and currents can exist without energy? Maybe an example
of EM voltage and EM current existing without ExB joules/sec
would help.
--
and yet again you cross up terms... voltage and current are on wires. E and
B are fields between or outside of wires. while they can be handled
similarly they should not be compared directly as you are asking. and yes,
there is at least one very good example of a voltage without ExB... just
charge a balloon up with some stray electrons and leave it alone long enough
to reach steady state... voila, E with no B. Please do this experiment and
reply when you have truly reached steady state.