Cecil Moore wrote in news7iPh.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

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

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

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

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

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

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.

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

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