Is the Superposition Principle invalid?
 

The folks on this newsgroup who argue that the concept
of reflected energy is invalid and only standing waves
exist seem forced to abandon the principle of
superposition which states that a system can be
analyzed by considering the components separately
and adding them later.

So does the Superposition Principle give us permission
to analyze the forward wave and the reflected wave
separately, or not?

An S-Parameter analysis obviously considers the
forward wave and reflected wave separately. Is such
an analysis invalid or simply honoring the rules set
forth in the Principle of Superposition?
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

The only dispute about superposition that I have observed is
that it does not apply to the computation of power which can
easily be demonstrated by the most trivial of examples.

Superposition of voltages and currents seems to be quite
accepted and is an excellent tool for circuit and transmission
line analysis.

....Keith

Is the Superposition Principle invalid?
 

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.
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

On Mar 30, 12:44 pm, Cecil Moore wrote:
The folks on this newsgroup who argue that the concept
of reflected energy is invalid and only standing waves
exist seem forced to abandon the principle of
superposition which states that a system can be
analyzed by considering the components separately
and adding them later.

So does the Superposition Principle give us permission
to analyze the forward wave and the reflected wave
separately, or not?

An S-Parameter analysis obviously considers the
forward wave and reflected wave separately. Is such
an analysis invalid or simply honoring the rules set
forth in the Principle of Superposition?
--
73, Cecil http://www.w5dxp.com


We have done extensive research here at Muppet Labs, and we can assure
you, the Superstition Principle is alive and well, especially with
regard to radio amateurs' analyses of transmission lines.

From the Labs,
Dr. Honeydew

Is the Superposition Principle invalid?
 

Cecil Moore wrote in news:oMdPh.4051$u03.1743
@newssvr21.news.prodigy.net:

So does the Superposition Principle give us permission

Cecil, would you state the superposition principle as you know it?

Owen

Is the Superposition Principle invalid?
 

Cecil Moore wrote:
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.

Cecil,

If you actually understood the way the Poynting Theorem works, you would
not waste your time worrying about ExB. It provides no useful
information in support of your wacky energy flow ideas.


Hint: Although the Poynting vector is defined as ExB, this is only a
flux. If you are interested in information relating to conservation of
energy it is necessary to integrate over a closed volume. The total
integral of the flux over the surface of that volume is then equal to
the rate of change of energy within the volume.

In your favorite example, where energy is coursing back and forth along
the two directions of a lossless transmission line, this integral over
any volume you choose will be exactly zero. 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. The same amount of energy exits the integration
volume as enters it. Only in the case where there is a source or where
there is loss will the Poynting energy calculation yield a non-zero value.

If you want further information you can check advanced textbooks such as
"Classical Electrodynamics" by Jackson or "Principles of Optics" by Born
and Wolf. I am sure there are many other references, but those are the
two I check almost daily.

73,
Gene
W4SZ

Is the Superposition Principle invalid?
 

Owen Duffy wrote:
Cecil, would you state the superposition principle as you know it?

I'll just quote Hecht on that. He gives the three
dimensional differential wave equation and follows it
up with a linear combination of individual waves in
an equation that cannot be reproduced here and says,

"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."

The unreproducible equation essentially says that the
total wave function is equal to the algebraic sum of
the individual wave functions.

Hecht goes on to treat the forward wave and reflected
wave as the "separate constituent waves", something
that we have been told by the "reflected waves don't
exist" gurus on this newsgroup, is an invalid thing
to do.

It seems to me that the superposition principle gives us
permission to consider the forward and reflected waves
separately and "algebraically sum" the results. That is
exactly what the S-Paramater analysis is based upon.
The S-Parameter analysis considers a1 to be the incident
forward wave and a2 to be the incident reflected wave.
They are treated separately and then "algebraically
summed".
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

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.

So net energy equals zero? So what! We are NOT discussing net
energy here. We are discussing the forward Poynting vector
and the reflected Poynting vector as described in "Fields and
Waves ...", by Ramo and Whinnery. The Superpositon Principle
gives us permission to do so and the final result is identical
to any other valid analysis. Why are you guys so irrationally
afraid of the wave reflection model? What is your ulterior
motive in denying the existence of reflected waves during
steady-state? It has seemingly turned into a steady-state
religion administered by the steady-state high priests.
--
73, Cecil http://www.w5dxp.com

Is the Superposition Principle invalid?
 

Cecil Moore wrote in news:p7iPh.3356$YL5.856
@newssvr29.news.prodigy.net:

Owen Duffy wrote:
Cecil, would you state the superposition principle as you know it?

I'll just quote Hecht on that. He gives the three
dimensional differential wave equation and follows it
up with a linear combination of individual waves in
an equation that cannot be reproduced here and says,

"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."

The unreproducible equation essentially says that the
total wave function is equal to the algebraic sum of
the individual wave functions.

Hecht goes on to treat the forward wave and reflected
wave as the "separate constituent waves", something
that we have been told by the "reflected waves don't
exist" gurus on this newsgroup, is an invalid thing
to do.

It seems to me that the superposition principle gives us
permission to consider the forward and reflected waves
separately and "algebraically sum" the results. That is
exactly what the S-Paramater analysis is based upon.
The S-Parameter analysis considers a1 to be the incident
forward wave and a2 to be the incident reflected wave.
They are treated separately and then "algebraically
summed"

Cecil, this is not a complete definition, and you have not related it to
the subject under discussion, tranmission lines, and the quantities that
are being discussed.

To my mind, there is nothing in YOUR definition above (it is not Hecht's,
it is your partical quote and elaboration) that states that it is valid
to sum energy waves or power waves (whatever those terms mean) as you
seem to want to do, or to treat them independently if that is what
'separately' means as you use it, or the specifics of what quantities are
summed.

Several people have been freely writing expressions that take the
algebraic sum of phasor quantities Vf and Vr, and If and Ir. You are
citing and partially quoting obscure sources not directly relevant to the
subject to justify your summation of energy waves or power waves or
whatever you are calling them today.

Sit down and write a complete definition of your knowledge of the
"Superposition Principle" as you understand it using quantities
encountered in a transmission line analysis, like voltage, current,
power.

Owen

Is the Superposition Principle invalid?
 

Owen Duffy wrote:
To my mind, there is nothing in YOUR definition above (it is not
Hecht's,
it is your partical quote and elaboration) that states that it is valid
to sum energy waves or power waves (whatever those terms mean) as you
seem to want to do, or to treat them independently if that is what
'separately' means as you use it, or the specifics of what quantities
are
summed.

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)

where A is the phase angle between the two energy waves.

This is the same as the irradiance equation from the field of
optics and applies perfectly to transmission lines. The first
time I saw the equation was in Dr. Best's QEX article so I
certainly cannot take credit for it.

All this information has been available on my web page for
years.
--
73, Cecil http://www.w5dxp.com