Cecil Moore wrote in newsMdPh.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

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

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

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

On Mar 30, 3:44 pm, Cecil Moore wrote:
So does the Superposition Principle give us permission
to analyze the forward wave and the reflected wave
separately, or not?

It would appear from the many posts that the consensus is
that superposition is alive and well. It works for voltages
and currents. It does not work for power.

But then I have two questions.

Firstly, in another thread, the solution for the problem
presented required knowing the impedance that the generator
presented to the reflected wave. This is exactly the sort
of question that superposition handles easily: The impedance
encountered by the reflected wave at the generator is the
same as the generator's source impedance. I am curious as to
why you don't want to use superposition to facilitate solving
this problem?

Secondly, the "directional wattmeter" uses superposition
to compute Vf and Vr from which it computes Pf and Pr. You,
like many others seem willing to subtract Pr from Pf to
obtain Pnet. But this would only seem to be valid if
superposition works for power. So why are people who accept
that superposition does not work for power, prepared to
accept that Pnet = Pf - Pr?

....Keith

Keith Dysart wrote:

The impedance
encountered by the reflected wave at the generator is the
same as the generator's source impedance.

No, the generator's source impedance is *NOT* the
impedance encountered by the reflected wave. Please
reference w2du's article again.

http://www.w2du.com/r3ch19a.pdf

Forget about the conjugate match and concentrate on the
non-dissipative source resistance being different from
what you are calling the generator's source impedance.
An *active* source creates a source impedance looking back
into the source that is *different* from what you are
calling the generator impedance.

Secondly, the "directional wattmeter" uses superposition
to compute Vf and Vr from which it computes Pf and Pr. You,
like many others seem willing to subtract Pr from Pf to
obtain Pnet.

One can directly add and subtract powers under certain
conditions. One condition is if two waves are not coherent.
Another condition is if two coherent waves have no effect
on each other. Since the forward wave and the reflected
wave have no effect on each other (except in the human
mind) reflected power can simply be subtracted from from
forward power to obtain power delivered to the load but
that is NOT superposition of powers. It is a simple
addition/subtraction of scalars based on the conservation
of energy principle.

But this would only seem to be valid if
superposition works for power. So why are people who accept
that superposition does not work for power, prepared to
accept that Pnet = Pf - Pr?

You seem to have forgotten the definition and rules of
superposition. Superposition applies to fields and waves.
Superposition doesn't apply to scalars. Power is a scalar.
Or another way to express it is:

V1 + V2 = V3 (vectors or phasors)

(V1 + V2)^2 = V3^2 (scalars)

V1^2 + V2^2 V3^2 (scalars)

It's a pretty simple principle of mathematics. The square
of the sum is NOT equal to the sum of the squares.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
V1 + V2 = V3 (vectors or phasors)

(V1 + V2)^2 = V3^2 (scalars)

In fact, the irradiance (power) equation falls out
directly from the above valid equation. Continuing
the process:

V1^2 + 2(V1)(V2) + V2^2 = V3^2

V1^2 + 2*SQRT(V1^2)*SQRT(V2^2) + V2^2 = V3^2

V1^2 + V2^2 + 2*SQRT(V1^2*V2^2) = V3^2

Dividing both sides of the equation by Z0 yields:

P1 + P2 + 2*SQRT(P1*P2) = P3

There you have it. The mathematical derivation of
the irradiance (power) equation.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
P1 + P2 + 2*SQRT(P1*P2) = P3

There you have it. The mathematical derivation of
the irradiance (power) equation.

This is, of course, for the condition where V1 and
V2 are in phase.
--
73, Cecil http://www.w5dxp.com