Tom Donaly wrote:

Cecil Moore wrote:
Seems the easiest measurement of nonlinearity would be the
harmonics (if any) generated by the antenna that do not
appear in the source signal.

Which wouldn't tell you a single thing about the current
distribution along the length of the dipole.

Yes it would. It would be proof that the current distribution
along the length of the dipole is sinusoidal no matter what
your illusionary perceptions are telling you.

For standing wave antennas, if the source is a pure single
frequency sine wave and if no harmonics are generated
by the antenna system:

1. The forward wave is sinusoidal.

2. The reflected wave is sinusoidal and coherent with the
forward wave.

3. Their superposition results in a sinusoidal standing wave
with the same angular velocity.

Any non-linearity would introduce harmonics.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil Moore wrote:
Tom Donaly wrote:

Cecil Moore wrote:

Seems the easiest measurement of nonlinearity would be the
harmonics (if any) generated by the antenna that do not
appear in the source signal.


Which wouldn't tell you a single thing about the current
distribution along the length of the dipole.


Yes it would. It would be proof that the current distribution
along the length of the dipole is sinusoidal no matter what
your illusionary perceptions are telling you.

For standing wave antennas, if the source is a pure single
frequency sine wave and if no harmonics are generated
by the antenna system:

1. The forward wave is sinusoidal.

2. The reflected wave is sinusoidal and coherent with the
forward wave.

3. Their superposition results in a sinusoidal standing wave
with the same angular velocity.

Any non-linearity would introduce harmonics.

The purpose of most antennas is to radiate electromagnetic waves.
That means there is loss. It also means that the current envelope is
affected. That's one of the reasons we use EZNEC. I suppose, Cecil,
that if you keep repeating the same old tired line, over and over
again, you might find someone who will agree with you. Certainly,
no antenna measurement would.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
The purpose of most antennas is to radiate electromagnetic waves.
That means there is loss. It also means that the current envelope is
affected. That's one of the reasons we use EZNEC.

The current envelope is affected but remains a linear
system function since it is the result of superposition
which itself is a linear system function.

I suppose, Cecil,
that if you keep repeating the same old tired line, over and over
again, you might find someone who will agree with you. Certainly,
no antenna measurement would.

The current envelope is a linear system function. I am
repeating the rules and laws of mathematics. Sounds
like you need to review the definition of linear systems.
You can do that at:

http://www.cns.nyu.edu/~david/linear...r-systems.html

In particular, quoting: "Systems that satisfy both homogeneity
and additivity are considered to be linear systems. These two rules,
taken together, are often referred to as the principle of superposition."

In general, antennas are linear systems that satisfy the principle
of superposition. If they were non-linear, they would not satisfy
the principle of superposition. Two linear system functions, like
forward waves and reflected waves, cannot superpose to a non-linear
function. Therefore, standing waves are linear, not non-linear,
functions. To argue otherwise exhibits a certain degree of ignorance.

Until the obvious mathematical misconception is corrected, no
rational discussion is possible. To the best of my knowledge,
Maxwell's equations are also linear system functions so claims
of non-linearity also contradict Maxwell's equations.
--
73, Cecil http://www.qsl.net/w5dxp

I suppose, Cecil,
that if you keep repeating the same old tired line, over and over
again, you might find someone who will agree with you.
=========================================

I agreed with Cecil the first time he said it.
But I'm only a foreigner.
So whatever I say doesn't carry any weight.
Or does it?
----
Reg.

Reg Edwards wrote:
I suppose, Cecil,
that if you keep repeating the same old tired line, over and over
again, you might find someone who will agree with you.

I agreed with Cecil the first time he said it.
But I'm only a foreigner.
So whatever I say doesn't carry any weight.
Or does it?

I dug out my linear network theory book and would like
to present a few quotes and comments:

"The real world is inherently non-linear."

Lightning hitting an antenna can cause arcing and melted
wires.

"Although nature is non-linear, linear approximations over
defined ranges of validity are valid representations of
non-linear phenomena."

Amateur radio antennas are usually confined to that limited
linear range.

"The necessary and sufficient conditions for a linear system
a (1) validity of the principle of superposition;
(2) preservation of scale factor.

Does doubling the power input to the antenna ~double the
radiated power? Does it ~double the non-radiated losses?

"Fortunately for the engineer, however, linear systems are
frequently excellent approximations to reality and have a
wide range of validity in the real world."

Maxwell's equations in particular. Textbook equations for
traveling waves and standing waves assume linearity.
--
73, Cecil http://www.qsl.net/w5dxp

Cecil Moore wrote:

Reg Edwards wrote:

I suppose, Cecil,
that if you keep repeating the same old tired line, over and over
again, you might find someone who will agree with you.


I agreed with Cecil the first time he said it.
But I'm only a foreigner.
So whatever I say doesn't carry any weight.
Or does it?


I dug out my linear network theory book and would like
to present a few quotes and comments:

"The real world is inherently non-linear."

Lightning hitting an antenna can cause arcing and melted
wires.

"Although nature is non-linear, linear approximations over
defined ranges of validity are valid representations of
non-linear phenomena."

Amateur radio antennas are usually confined to that limited
linear range.

"The necessary and sufficient conditions for a linear system
a (1) validity of the principle of superposition;
(2) preservation of scale factor.

Does doubling the power input to the antenna ~double the
radiated power? Does it ~double the non-radiated losses?

"Fortunately for the engineer, however, linear systems are
frequently excellent approximations to reality and have a
wide range of validity in the real world."

Maxwell's equations in particular. Textbook equations for
traveling waves and standing waves assume linearity.

You can still pretend a dipole is a "linear system," as you
call it, and still understand that the current envelope is not
a simple sine function. The Achilles heel of all your reflection
mechanics ideas is the assumption that everything is lossless.
(Not to mention the fact that it's supposed to exist in outer
space.) You and Reg like to think of a dipole as a transmission line,
and Reg can even tell you its characteristic impedance (average). What
neither he nor you ever mention is the alpha part of the
propagation constant. That's the important part, though, since it
signifies radiation, the very thing the antenna was designed to do.

By the way, why are you quoting from a network theory book when not
too long ago you were ranting and raving about the invalidity of the
lumped constant model?
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
You can still pretend a dipole is a "linear system," as you
call it, and still understand that the current envelope is not
a simple sine function.

Diverting to a "simple" sine function in the same spirit as
diverting to a "small" loading coil?

If you were always talking about a perfect sine wave, you should
have said so long before now and nobody would have disagreed with
you.

The Achilles heel of all your reflection
mechanics ideas is the assumption that everything is lossless.

That's NOT the assumption. The assumption is that lossless systems
are easiest to understand so let's understand them first before
we move on to something more complex. You guys have proven that
you don't even understand the simple lossless condition.

(Not to mention the fact that it's supposed to exist in outer
space.) You and Reg like to think of a dipole as a transmission line,
and Reg can even tell you its characteristic impedance (average). What
neither he nor you ever mention is the alpha part of the
propagation constant. That's the important part, though, since it
signifies radiation, the very thing the antenna was designed to do.

Only about 1 dB of the steady-state energy stored in a 1/2WL
dipole is radiated so radiation is not the largest effect. The
radiation from an antenna can be simulated by using resistance
wire to simulate a 1 dB loss in a transmission line. The reason
that I have rarely mentioned such is that you guys don't understand
enough of the basics to proceed to those more complex examples.

By the way, why are you quoting from a network theory book when not
too long ago you were ranting and raving about the invalidity of the
lumped constant model?

The lumped constant model is valid under certain conditions. What I
object to is its use under known invalid conditions. The lumped constant
model and distributed network model are both *linear systems*.
--
73, Cecil http://www.qsl.net/w5dxp

Reg Edwards wrote:
I suppose, Cecil,
that if you keep repeating the same old tired line, over and over
again, you might find someone who will agree with you.

=========================================

I agreed with Cecil the first time he said it.
But I'm only a foreigner.
So whatever I say doesn't carry any weight.
Or does it?
----
Reg.



You're the master of simple approximation, Reg. Cecil thinks
your simplified ideas are received wisdom. Knowing you,
I find it hard to believe you'd ever agree with anyone.
73,
Tom Donaly, KA6RUH

Tom Donaly wrote:
Knowing you,
I find it hard to believe you'd ever agree with anyone.

Reg and I are in perfect agreement on the benefits
of a good Cabernet.
--
73, Cecil http://www.qsl.net/w5dxp

On Sat, 20 May 2006 17:39:44 GMT, "Tom Donaly"
wrote:

Cecil thinks your simplified ideas are received wisdom.

Hi Tom,

Is there some suggestion of smoldering bush in this parable?
Commandments that are unzipped and ready for immediate entablature?

73's
Richard Clark, KB7QHC