On Thu, 18 May 2006 03:32:49 GMT, Cecil Moore
wrote:
Antennas are linear systems.
another list game, hmm?
Antennas are wires in the sky;
Antennas are fun;
Antennas are this,
....that,
....and,
....another.

I would amend Cecil's statement to:
'We hope antennas are linear systems.'

A nonlinear antenna is a terrible beast indeed. It will mix every
signal it receives with every other signal, creating a nasty mush of
signals. On transmit it is not so bad, maybe generating harmonics and
a wider signal than we'd like.

We've all heard stories of a poor antenna connection causing problems,
or a nearby raingutter joint causing TV inteference. These are
nonlinear antennas.

73,
Glenn AC7ZN

On 18 May 2006 08:42:06 -0700, wrote:

I would amend Cecil's statement to:
'We hope antennas are linear systems.'

A nonlinear antenna is a terrible beast indeed. It will mix every
signal it receives with every other signal, creating a nasty mush of
signals. On transmit it is not so bad, maybe generating harmonics and
a wider signal than we'd like.

We've all heard stories of a poor antenna connection causing problems,
or a nearby raingutter joint causing TV inteference. These are
nonlinear antennas.

Hi Glenn,

Cecil is being deliberately obtuse to the matter of linearity. In the
game of describing an antenna as a transmission line, the
non-linearity is compellingly obvious.

If you start with standard twin line, its characteristic Z is
dominated by geometry and a ratio of wire diameter to wire separation.
Pull that twin line apart to construct a V or a dipole, and the
geometry necessarily forces a non-linearity into the picture.

Reggie also has considerable difficulty with this concept too as he
prefers to switch to earth as the main arbiter of transmission line
dynamics. Both seem to abandon the generator's view of a 50 to 70 Ohm
load to replace it with their 600 Ohm concepts so as to artificially
impose their need to see a linear load.

These 600 Ohm concepts are achieved only if the operator strains to
fail most spectacularly. Few debates are won this way, but arguments
successfully persist for hundreds of postings. Even then, these
concepts do not answer the initial non-linearity that inhabits the
system. Both the 50 to 70 to 600 Ohm prognostications are artifacts
of a measurement at the terminal of the non-linear device.

The proof lies along the line, and this returns us to the underlying
concept and argument about the distribution of current along the
length of the quarter wave dipole's arms. This is stated in terms of
the Cosine function. However, as with a deliberate failure forcing an
erroneous general solution, the Cosine distribution is only found in
the extreme (or the fevered dream). A 1mm wire strung 36 meters in
outer space is certainly thin by engineering conventions, but it
doesn't qualify as the current distribution misses the mark of
Cosinality by 5 or 6% (the distribution of a poor fit demonstrates the
non-linearity).

Given Cecil's penchant for abstracting considerable error to general
proofs of his crystalline logic, this may not seem much. However, the
precision above is not outside of achievement, and it does demonstrate
with simplicity that linearity does not reside in the
transmission-line-as-antenna. Pulling this antenna down to earth to
allow the boys their investment in the 600 Ohm concepts does nothing
to recover linearity - if anything, it worsens it (albeit, by very
slim margins). Clearly, the dominant factor in the linearity of the
dipole's characteristic Z is with its own wire. This has been long
reported in the literature (Schelkunoff).

Further, to anticipate this does not demonstrate any spurious
emissions - this is only due to your (not yours, Glenn, your in the
sense of the general reader, and our boys with their loss of
investment) inability to resolve them.

This class of non-linearity falls under the heading of "scattering"
and in these most mundane of applications would barely present
spurious products higher than 70dB below excitation, and only several
parts-per-million from the center frequency (called Stokes shift).
When Cecil comes to the table armed with slop on the order of ±59%
allowable error, such products are swamped in stupidity.

73's
Richard Clark, KB7QHC

"Richard Clark" wrote:
In the
game of describing an antenna as a transmission line, the
non-linearity is compellingly obvious.

A non-linear system would generate harmonics so where are
those harmonics?

A 1mm wire strung 36 meters in
outer space is certainly thin by engineering conventions, but it
doesn't qualify as the current distribution misses the mark of
Cosinality by 5 or 6% (the distribution of a poor fit demonstrates the
non-linearity).

Nobody said it was a perfectly ideal cosine curve. You seem to have
a strange definition of non-linearity as anything that differs from the
ideal. By that definition, everything is non-linear (including your
definition).
The definition of non-linearity being used here is "discontinuous".
Exactly where does the current in an antenna become discontinuous?

Heaven forbid the cosine curve exhibit the same accuracy as a resistor.
Would you also assert that a 52 ohm resistor that is marked 50 ohms is
exhibiting non-linearity?
--
73, Cecil, W5DXP

"Cecil Moore" wrote:
The definition of non-linearity being used here is "discontinuous".
Exactly where does the current in an antenna become discontinuous?

For readers who don't understanding the meaning of "linear systems",
here is a tutorial:

http://doctord.dyndns.org:8000/cours...ar_Systems.htm
--
73, Cecil, W5DXP

On Thu, 18 May 2006 20:04:12 GMT, "Cecil Moore"
wrote:
A non-linear system would generate harmonics so where are
those harmonics?

There's no need to repeat one post removed coverage so early.

Richard,

Wow. You spent a lot of time on this. Thanks.

Let's abandon antennas and postulate a twin-lead vacuum-dielectric 100
ohm transmission line that is ideal in the respects we consider
important (except loss). There may be (resistive) loss, but no
coupling to outside sources or objects, no hysteresis, no
electromagnetic radiation. The characteristic impedance is exactly 100
ohms real over our frequency of interest. The velocity factor, for
convenience, is 0.5.

We feed it on one end with a sinewave generator whose impedance is
matched to the line. On the other end we terminate the line with a
floating load of arbitrary impedance. The only requirement of the load
is that it be perfectly linear and can be described completely as a
real and imaginary impedance at any given frequency of interest.

Would you consider this system linear? We are not talking antennas
now...nothing is radiating.

I'm not sure I'm going to go anywhere with this, and I'm not setting a
trap. I'm just curious what conditions would have to be set before you
would consider a transmission line system linear (you are welcome to
add any conditions I might have forgotten). By the way, if you want to
discuss any really subtle effects such a Stokes shifting, I define
linearity as obeying the law of superposition within a reasonable
dynamic range, say 140 dB, which is about 20 dB better than the input
dynamic range of our best HF receivers.

I understand you are in an argumentative mood with others in the group,
but I am taking no sides (I do happen to like Cecil's motorbike...) and
will try to keep things civil. If I go anywhere with this, I hope to
explain it clearly enough and with enough supporting material that
there will be no arguments. I am not a guru so don't expect anyone to
believe anything on my word alone.

So what say you Richard? Do we have linearity?

73,
Glenn AC7ZN

On 18 May 2006 13:52:52 -0700, wrote:

Wow. You spent a lot of time on this. Thanks.

Hi Glenn,

Most of this time has long preceded these posts (by as many years as
Reggie has been posting here).

Would you consider this system linear?

Yes.

I'm not sure I'm going to go anywhere with this, and I'm not setting a
trap. I'm just curious what conditions would have to be set before you
would consider a transmission line system linear (you are welcome to
add any conditions I might have forgotten).

I see no reason to constrain an open-ended topic; your definition is
fairly self referential after all:
I define X as a linear system;
Is X linear?

What correspondence that follows may upset the apple-cart, but aside
from the velocity factor gaff (which bears no relation, yet, on
linearity), I have no dispute.

What could upset the apple cart? Power.

Power has the capacity to distort systems and introduce
non-linearities even in your simple example. If I were to expand upon
what you call the subtle effects (they were in my earlier discussion);
this would give rise to back-scattering which could power limit the
line (in other words, it could never deliver more than a baseline
value). The onset of this condition is, again, nothing anyone here
has ever experienced, and to even approach this limit in the lines you
have constructed would tax most sources.

Such topics that may appear to be new here, have been exhibited in
fiber optic transmission lines for quite a while now.

73's
Richard Clark, KB7QHC

Glenn, can you understand whatever it is poor, demented Richard is
waffling about?

Richard Clark wrote:

On 18 May 2006 08:42:06 -0700, wrote:


I would amend Cecil's statement to:
'We hope antennas are linear systems.'

A nonlinear antenna is a terrible beast indeed. It will mix every
signal it receives with every other signal, creating a nasty mush of
signals. On transmit it is not so bad, maybe generating harmonics and
a wider signal than we'd like.

We've all heard stories of a poor antenna connection causing problems,
or a nearby raingutter joint causing TV inteference. These are
nonlinear antennas.


Hi Glenn,

Cecil is being deliberately obtuse to the matter of linearity. In the
game of describing an antenna as a transmission line, the
non-linearity is compellingly obvious.

If you start with standard twin line, its characteristic Z is
dominated by geometry and a ratio of wire diameter to wire separation.
Pull that twin line apart to construct a V or a dipole, and the
geometry necessarily forces a non-linearity into the picture.

Reggie also has considerable difficulty with this concept too as he
prefers to switch to earth as the main arbiter of transmission line
dynamics. Both seem to abandon the generator's view of a 50 to 70 Ohm
load to replace it with their 600 Ohm concepts so as to artificially
impose their need to see a linear load.

These 600 Ohm concepts are achieved only if the operator strains to
fail most spectacularly. Few debates are won this way, but arguments
successfully persist for hundreds of postings. Even then, these
concepts do not answer the initial non-linearity that inhabits the
system. Both the 50 to 70 to 600 Ohm prognostications are artifacts
of a measurement at the terminal of the non-linear device.

The proof lies along the line, and this returns us to the underlying
concept and argument about the distribution of current along the
length of the quarter wave dipole's arms. This is stated in terms of
the Cosine function. However, as with a deliberate failure forcing an
erroneous general solution, the Cosine distribution is only found in
the extreme (or the fevered dream). A 1mm wire strung 36 meters in
outer space is certainly thin by engineering conventions, but it
doesn't qualify as the current distribution misses the mark of
Cosinality by 5 or 6% (the distribution of a poor fit demonstrates the
non-linearity).

Given Cecil's penchant for abstracting considerable error to general
proofs of his crystalline logic, this may not seem much. However, the
precision above is not outside of achievement, and it does demonstrate
with simplicity that linearity does not reside in the
transmission-line-as-antenna. Pulling this antenna down to earth to
allow the boys their investment in the 600 Ohm concepts does nothing
to recover linearity - if anything, it worsens it (albeit, by very
slim margins). Clearly, the dominant factor in the linearity of the
dipole's characteristic Z is with its own wire. This has been long
reported in the literature (Schelkunoff).

Further, to anticipate this does not demonstrate any spurious
emissions - this is only due to your (not yours, Glenn, your in the
sense of the general reader, and our boys with their loss of
investment) inability to resolve them.

This class of non-linearity falls under the heading of "scattering"
and in these most mundane of applications would barely present
spurious products higher than 70dB below excitation, and only several
parts-per-million from the center frequency (called Stokes shift).
When Cecil comes to the table armed with slop on the order of ±59%
allowable error, such products are swamped in stupidity.

73's
Richard Clark, KB7QHC

Thanks a lot for this one, Richard.

And of course, Cecil has already ignored the important bits and state4d
that 6% is no big deal. Typical.

As I said earlier, the responses to Cecil are where the gold resides.

I had not heard of the Stokes shift, nor the scattering you mentioned.
I have some looking up and reading to do. Which, of course, Cecil does
not, since it's not a Xerox moment.

tom
K0TAR