Joel Koltner wrote:
"Powers don't add, field strengths do"

"Add" is a rather loosely defined term. A more technically
precise statement would be: "Powers don't superpose, field
strengths do." When fields superpose, they still must obey
the conservation of energy principle, i.e. the total energy
before the superposition must equal the total energy after
the superposition.

Given two RF waves in a transmission line and the phase angle,
A, between the two electric fields, the following Power equation,
published in QEX, gives us a valid method of "adding" two powers.

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

Reference: "Wave Mechanics of Transmission Lines, Part 3",
by Steven R. Best, VE9SRB, "QEX", Nov/Dec 2001, (Eq 13),
page 4.

The last term is known in optics as the "interference"
term, positive for constructive interference and negative
for destructive interference. Angle A, the phase angle
between the two electric fields, determines the sign
of the last term and thus whether interference is
destructive or constructive.

Reference: "Optics", by Hecht, 4th Edition:
Chapter 7: The Superposition of Waves
Chapter 9: Interference
--
73, Cecil http://www.w5dxp.com

"Cecil Moore" wrote in message
...
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

So... let's see... my two 1/2W antennas now, in the "preferred" location, get
you... 0.5+0.5+2*sqrt(0.5*0.5)*cos(0) = 2W... yep, same as the field strength
analysis. Cool!

Presumably you could demonstrate all this with a "ripple tank" (the kind with
water used back in high school physics) -- set things up so that, in a
preferred direction, the wave height is 1.414 even though the wave height made
by each "radiator" in isolation is 0.707.

Thanks Cecil,
---Joel

Cecil Moore wrote:
Joel Koltner wrote:
"Powers don't add, field strengths do"

"Add" is a rather loosely defined term. A more technically
precise statement would be: "Powers don't superpose, field
strengths do."

Fields superpose, numbers add, and power is the rate of change in energy.

When fields superpose, they still must obey
the conservation of energy principle, i.e. the total energy
before the superposition must equal the total energy after
the superposition.

It's almost as if you think that if you don't always point it out,
energy won't be conserved! :-)

Given two RF waves in a transmission line and the phase angle,
A, between the two electric fields, the following Power equation,
published in QEX, gives us a valid method of "adding" two powers.

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

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position. It's
just that there's no valid way to multiply by the cosine of the angle
between two scalars.

Maybe wave problems are best solved using waves.

The last term is known in optics as the "interference"
term, positive for constructive interference and negative
for destructive interference. Angle A, the phase angle
between the two electric fields, determines the sign
of the last term and thus whether interference is
destructive or constructive.

(A+B)*(A+B) = A^2 + B^2 + 2AB

Must the first order term (2AB) in such equations always be referred to
as "The Interference Term", Cecil? Doing so seems to impart a greater
level of importance to it than to the other, unnamed terms in the
equation. The factored form must then be least important of all.

Beats, interference, and modulation are fundamentally the same
phenomenon. There's no need to get all worked up about one of them in
deference to the others, just as there's no need to worry about there
being a node for every antinode.

73, ac6xg

Jim Kelley wrote:
Cecil Moore wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position. It's
just that there's no valid way to multiply by the cosine of the angle
between two scalars.

You are pretty confused. The angle is between the electric
field intensities of the two waves being superposed.

Must the first order term (2AB) in such equations always be referred to
as "The Interference Term", Cecil?

From "Optics", by Hecht, 4th Edition, page 387 & 388:

"I12 = 2E1*E2 ... and is known as the interference term."
E1 and E2 are electric field intensities. * is the dot product.
indicates a time average value.

"The interference term becomes I12 = 2*SQRT(I1*I2)cos(delta)"

Hecht calls it the "interference term" and I am only quoting
him.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Jim Kelley wrote:
Cecil Moore wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position.
It's just that there's no valid way to multiply by the cosine of the
angle between two scalars.

You are pretty confused.

I think you know that I'm just pointing out the problem inherent in
using a valid equation in the way you describe without considering the
many assumptions being made. It led you, for example, to write that
there is a 4th mechanism of reflection - even in violation of Maxwell's
equations! Do you still believe that interference actually moves power
from one place to another? It is that kind of nonsense that amateur
radio would be better off without.

Hecht calls it the "interference term" and I am only quoting
him.

I'll bet he'd prefer that you didn't. :-)

73, ac6xg

Jim Kelley wrote:
I think you know that I'm just pointing out the problem inherent in
using a valid equation in the way you describe without considering the
many assumptions being made. It led you, for example, to write that
there is a 4th mechanism of reflection -

Here's a quote from my energy article:

"Note that the author previously used the word "reflection" for both
actions involving a single wave and the interaction between two waves.
Now the word "reflected" is being used only for single waves and the
word "redistributed" is being used for the two wave interference scenario."

Nowhere in my present article do I say there is a 4th mechanism
of reflection. Why do you continue to incessantly harp on past
semantic blunders that were corrected years ago?

Do you still believe that interference actually moves power
from one place to another?

Do you ever stop beating dead horses? :-)

Since I stated in my article that power doesn't flow, you are just
once more bearing false witness. Maybe you should have that burr
under your blanket looked at by a competent veterinarian. :-)

I said that the redistribution of energy, which necessarily obeys
the conservation of energy principle, is associated with a wave
cancellation interference event. I never uttered your false
statement that "interference moves power". Here's what I said:

"The term "power flow" has been avoided in favor of "energy flow".
Power is a measure of that energy flow per unit time through a
plane. Likewise, the EM fields in the waves do the interfering.
Powers, treated as scalars, are incapable of interference."

Yet, a couple of times a year just like clockwork, you accuse
me of saying that power moves (which I have never said). One
wonders what drives your never-ending vendetta obsession.

Here is the definition that I am using for RF "interference"
adopted from "Optics", by Hecht:

RF wave interference corresponds to the interaction of two
(or more) RF waves yielding a resultant power density for
the total wave that deviates from the sum of the two power
densities in the superposed component waves.

It is simple physics to realize that (V1+V2)^2 is not usually
equal to (V1^2 + V2^2). When they are not equal, interference
has occurred. Why do you have such a problem with such a simple
concept?

In a transmission line, the power equation indicates exactly
by how much the resultant power deviates from the sum of the
component powers. The magnitude of that deviation from the
sum of the component powers is called the "interference term"
according to Hecht.

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

'A' is the angle between the V1 and V2 voltage phasors.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Jim Kelley wrote:

Do you still believe that interference actually moves power
from one place to another?

Since I stated in my article that power doesn't flow, you are just
once more bearing false witness.

Let me try this then: Do you still think that interference is what
moves ENERGY from one place to another?

"The term "power flow" has been avoided in favor of "energy flow".

Yet, a couple of times a year just like clockwork, you accuse
me of saying that power moves (which I have never said). One
wonders what drives your never-ending vendetta obsession.

Note that the reason the author included the disclaimer about "power
flow" was because the term "power flow" had not been avoided by said
author in this newsgroup, in an argument which must have gone on for 6
weeks. In fact, it was a point that was never actually conceded.
Rather, thusly, he "avoided" conceding it. (Reminder: Now you come back
by mentioning how Poynting vectors show how much and in which direction
the power is flowing.)

It is simple physics to realize that (V1+V2)^2 is not usually
equal to (V1^2 + V2^2). When they are not equal, interference
has occurred.

Well, 8th grade algebra is supposed to help us realize that (V1+V2)^2 is
not equal to (V1^2 + V2^2). But the fact that (V1+V2)^2 is equal to
V1^2 + V2^2 + 2V1*V2 doesn't depend in the least on whether
"interference has occurred", Cecil. That was the whole point of my
comment about it.

In a transmission line, the power equation indicates exactly
by how much the resultant power deviates from the sum of the
component powers. The magnitude of that deviation from the
sum of the component powers is called the "interference term"
according to Hecht.

You'd think it would be enough for someone to throw out the whole idea
of "the sum of the powers" once and for all. But no. The inclination
instead is apparently to keep refining one's epicycle formulary. Hecht
makes no such connection between 'power' and 'interference', Cecil. And
why would he? There isn't one.....except in certain amateur radio
articles and newsgroup postings.

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

'A' is the angle between the V1 and V2 voltage phasors.

....and NOT between the two 'powers'. Still, it's a very useful
expression for finding a quick, albeit simplified solution. That is
after all its intended purpose.

73, ac6xg

Jim Kelley wrote:
Let me try this then: Do you still think that interference is what
moves ENERGY from one place to another?

To the best of my knowledge, I addressed all of your objections
in a revision to my energy article which was done many months
ago. The reasons for your objections don't even exist any more.

Note that the reason the author included the disclaimer about "power
flow" was because the term "power flow" had not been avoided by said
author in this newsgroup, in an argument which must have gone on for 6
weeks.

But that argument happened many, many years ago. You convinced
me that power doesn't flow. I respect the fact that it is a
commonly accepted concept defined in "The IEEE Dictionary",
rampant within every power company, and accepted by many
members of this newsgroup.

If you will check back over the years, you will find a posting
of mine where I said the dimensions of power flow would be
joules/sec/sec which doesn't make any physical sense.

But the fact that (V1+V2)^2 is equal to
V1^2 + V2^2 + 2V1*V2 doesn't depend in the least on whether
"interference has occurred", Cecil. That was the whole point of my
comment about it.

Yes, and you are still wrong according to Hecht. If the
interference term in the power equation is not zero,
(V1^2+V2^2) does not equal (V1+V2)^2. In the special case
where (V1^2+V2^2) = (V1+V2)^2, the interference
term is zero, i.e. zero interference.

Please reference page 388 in "Optics", by Hecht, 4th Edition.

Hecht
makes no such connection between 'power' and 'interference', Cecil.

But Hecht certainly makes a connection between 'power density' and
'interference'. It is a trivial matter to convert the power density
irradiance equation to the power equation by multiplying by the
cross-sectional area of a transmission line.

The units of irradiance (power density) are joules/sec/unit-area.

Multiply the irradiance equation by the unit-area of the coax,
e.g. 1 in^2, and you get joules/sec = power which is what a
Bird wattmeter indicates.

If you want, you can convert the Bird wattmeter reading to
irradiance by dividing by the cross-sectional area of the
coax.

'A' is the angle between the V1 and V2 voltage phasors.

...and NOT between the two 'powers'.

*Nobody* has ever said there is a phase angle between two powers
yet you persist in that false strawman implication.
--
73, Cecil http://www.w5dxp.com

Jim Kelley wrote:
Cecil Moore wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position. It's
just that there's no valid way to multiply by the cosine of the angle
between two scalars.

I suspect you knew if I ever found my Born and Wolf after my
move, you would be in trouble - and you are.

You previously said that Born and Wolf did not agree with
Hecht, but they do, contrary to your assertions.

Their equation for irradiance (intensity) agrees with Hecht.

Itot = I1 + I2 + J12

where J12 = 2E1*E2 = 2*SQRT(I1*I2)*cos(A)

On page 258 of "Principles of Optics", by Born and Wolf,
4th edition, they label J12 as the *interference term*,
contrary to your assertions. (Hecht labels that term I12)
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:
Jim Kelley wrote:
Cecil Moore wrote:
Ptotal = P1 + P2 + 2*SQRT(P1*P2)*cos(A)

According to fig. 7.1 in Born and Wolf, that's useful for showing how
light intensity varies as a function of phase, and hence position.
It's just that there's no valid way to multiply by the cosine of the
angle between two scalars.

I suspect you knew if I ever found my Born and Wolf after my
move, you would be in trouble - and you are.

No. I assumed you could find fig 7.1 and see it for yourself. The plot
has phase on the X-axis and intensity on the Y-axis. The caption reads
Interference of two beams of equal intensity; variation of intensity
with phase difference. " At the top of the page: "Let us consider the
distribution of intensity resulting from the superposition of two waves
which are propagated in the z-direction...."

The relation is useful for precisely the reason I indicated. That is
why Heckt also includes it in his book.

I deleted the rhetorical blithering from your post. And again, please
quote my remarks directly whenever you wish to discuss them.

73, ac6xg