Joel Koltner wrote:
"Roy Lewallen" wrote in message
treetonline...
Not by a long shot! Here's a simple example from the EZNEC demo program,
using example file Cardioid.EZ. It's a two element array of quarter
wavelength vertical elements spaced a quarter wavelength apart and fed with
equal currents in quadrature to produce a cardioid pattern. The impedance of
a single isolated element is 36.7 + j1.2 ohms. In the array, the impedances
are 21.0 - j18.7 and 51.6 + j20.9 ohms, and the elements require 29 and 71
percent of the applied power respectively in order to produce equal fields.
The deviation is due to mutual coupling.

That's a much, much greater difference than I would have guessed. Wow...

Isn't the input impedance of one element affected not only by the relative
position of the other element, but also how it's driven? I.e., element #1
"sees" element #2 and couples to it, but how much coupling occurs depends on
whether the input of element #2 is coming from a 50 ohm generator vs. a 1 ohm
power amplifier (close to a voltage source), etc.? (Essentially viewing the
antennas as loosely coupled transformers, where the transformer terminations
get reflected back to the "primary.")

Not directly. What counts (considering the simple case of two elements)
is the magnitude and phase of the current in the other element, and
their spacing, orientation, and lengths. A good way to look at the
effect of mutual coupling is as "mutual impedance", i.e., the amount of
impedance change caused by mutual coupling. (Johnson/Jasik covers this
concept well.) If you were to feed two elements with constant current
sources (as in the Cardioid.EZ EZNEC example), mutual coupling doesn't
change the element currents, but only the feedpoint impedances. With any
other kind of feed system, the impedance change causes the currents to
change, which in turn affects the impedances. So the feed method
certainly does have an effect on the currents you get, which affects
both mutual coupling and pattern.

There's a lot more about this, and how to design feed systems which will
effect the desired currents, in the _ARRL Antenna Book_.

Thanks for the book links. Do you happen to have a copy of "Small Antenna
Design" by Douglas Miron? And have an opinion about it? Or some other book
on electrically small antennas? (Not phased arrays, though :-) -- more like
octave bandwidth VHF or UHF antennas that are typically 1/10-1/40 lambda in
physical size.)

I just recently purchased Miron's book but haven't yet looked at it in
any depth. It appears to be most interesting to anyone wanting a better
understanding of method of moments numerical methods. If you can read
German, you might be interested in _Kurze Antennen_ by Gerd Janzen. But
your search for small, broadband antennas puts you bump-up against the
principle "small - broadband - efficient, choose any two". They'll be
inefficient, which will hurt you both receiving and transmitting at VHF
and above. The book I'd go to for researching the possibilities would be
Lo & Lee's _Antenna Handbook_. You might also get some ideas from
Bailey, _TV and Other Receiving Antennas_, since TV antennas have to be
pretty broadband.

Roy Lewallen, W7EL

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

Cecil Moore wrote:
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.

May we assume that the term "4th mechanism of reflection" will be
avoided in future publications?

You convinced me that power doesn't flow.

Thank you, Jesus.

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.

Well, Hecht and I both understand the 8th grade algebra, and I don't
disagree with him. How then could he disagree with me? I think that's
the symmetric equality property. :-)

One possible way to resolve the apparent dichotomy would be to suppose
that you misunderstand what we are each saying.

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.

Which of course explains how it is that your answers come out correctly.
I believe I already mentioned that it does (obviously) produce correct
answers, given all the underlying assumptions are correct.

By the way, what assumptions are you making?

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

Wouldn't I first have to buy into the idea that power is flowing through
it? :-)

'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.

It's hard to imagine how a simple, mutually agreed upon statement of
fact could be construed as a "false strawman implication", but there it is.

73, ac6xg

Jim Kelley wrote:
May we assume that the term "4th mechanism of reflection" will be
avoided in future publications?

Yes, exactly as it has been for the past six months since
I revised my article. In less time than it takes to condemn
me for saying something in the far distant past, you could
have just read my article. Here's the half-year old footnote
from my article.

[10] Revision 1.1, Feb. 20, 2008 - In the original version, the
redistribution of energy due to wave cancellation was dubbed a
"reflection". W5DXP has dropped that designation in favor of a
"redistribution" as described by the FSU web page. The word "reflection"
is reserved for describing something that happens to a single wave when
it encounters an impedance discontinuity. The word "redistribution" of
energy is adopted for describing what happens to the energy in canceled
waves. In like manner, since interference can occur with or without wave
cancellation, any reference to interference as the cause of the
redistribution of energy has been removed.

You convinced me that power doesn't flow.

Thank you, Jesus.

That was at least eight years ago, Jim. What is wrong with
you? I have no doubt that six months from now, you will again
be accusing me of believing that power flows. You seem to be
suffering from dementia.

Which of course explains how it is that your answers come out correctly.
I believe I already mentioned that it does (obviously) produce correct
answers, given all the underlying assumptions are correct.

However, correct answers don't seem to be enough for you.
You seem to be looking for a stone tablet handed down from God.

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

Wouldn't I first have to buy into the idea that power is flowing through
it? :-)

No, irradiance, like power, doesn't flow. If you don't know
that, that's probably the source of your confusion.

It's hard to imagine how a simple, mutually agreed upon statement of
fact could be construed as a "false strawman implication", but there it is.

Your multiple unethical attempts to imply that I said power
has a phase angle is more than obvious to everyone.
--
73, Cecil http://www.w5dxp.com

Cecil Moore wrote:

What is wrong with
you?

Glutton for punishment I guess. Thanks for asking.

73, ac6xg