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

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

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

Your Freudian slip concerning your feelings about Hecht
is more than apparent, i.e. "To Heck with Hecht"! :-)

One wonders why you said something to the effect that
Hecht had been discredited in favor of Born and Wolf.
When I recommended the 57 page chapter on interference
in "Optics", by Hecht, you said something to the effect
that interference is unimportant, yet Born and Wolf's
chapter on interference is 113 pages long and mostly
agrees with Hecht's writings.
--
73, Cecil http://www.w5dxp.com

On Thu, 7 Aug 2008 17:55:29 -0700, "Joel Koltner"
wrote:

I've taken college classes in antennas and hence have a pretty good feel for
some of the mathematics behind it all, but I've found that at times I don't
have good, intuitive explanations for various antenna behaviors -- and I'm not
at all good at being able to look at some fancy antenna and start rattling off
estimates of the directivity, front to back ratio, etc. -- so I wanted to ask
a simple question on a two-element phased array:

First, start with one antenna. Feed it 1W, and assume that in some
"preferred" direction at some particular location the (electric) field
strength is 1mV/m.

Now, take two antennas, and space them and/or phase their feeds such that in
the same preferred direction the individual antenna patterns add. I.e., we're
expecting a 6dB gain over the single antenna (but only at that location).
Since we start off by splitting the power to each antenna (1/2W to each), that
initially seems impossible, since 1/2W+1/2W = 1W -- should imply the same
1mV/m field strength. But this is an incorrect analysis, in that powers don't
add directly. Instead, the fields add... hence, each antenna alone will now
produce 707uV/m (at the one particular location in question), so the two
together produce 1.414mV/m which is the same as if the single antenna had been
fed with 2W. Hence the 6dB gain we're after! (This analysis also implies
there must be other locations that now receive 1mV/m in order to conserve
energy.)

Is that correct? "Powers don't add, field strengths do" is obvious enough,
but definitely leads to some slightly non-intuitvely-obvious (to me) results.
By extension of the above, though, it becomes obvious that (in theory) one can
build an array with any desired amount of gain, the beamwidth just has to
become narrower and narrower, of course.

Thanks,
---Joel

What Roy did not tell you is that his program has a free demo version
(http://eznec.com/) that will will provide quick answers. The learning
curve for EZNEC is pretty sharp for about 10 minutes and then it
shallows out.

John Ferrell W8CCW