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On Fri, 19 May 2006 16:01:53 -0500, (Richard
Harrison) wrote:

"Because of this nonlinear characteristic of the dynamic curve over the
operating range, the wave form of the output wave differs slightly from
that of the grid-exciting-voltage waveshape. Distortion of this type is
called "nonlinear" or "amplitude" distortion.."

Hi Richard,

This harkens back to your observation about how many places in Pi.

How much distortion has to exist before you hear it? As this directly
relates to your quoted selection, are we to believe that distortion
does not exist if you cannot perceive it?

This gives a great range of flexibility to the word linear through the
careful selection for tone-deaf judges.

Back in the late 40s, Bell labs experimented with human subjects'
ability to discern distortion. Turns out that they could take quite a
bit (10 to 15%) before they could faithfully call it noticeable. So,
by these stricter standards (Cecil would allow 59% before ringing the
alarm) no distortion exists below 10%.

All of the antennas I`ve worked with had no noticeable amplitude
distortion. They caused no harmonics or mixing products.

No noticeable "amplitude" distortion? In a world of possible
distortions, does linearity boil down to just one metric? Are you
asking us to believe you anticipated any antenna would be non-linear
and purposely tested them all? Nah, this is wholly unreasonable.

Richard, I frankly doubt you looked for spurs that would have been
70dB down in the worst of circumstances. More overwhelming would be
corroded joints swamping that pursuit.

On page 235 of Kraus` 1950 edition of "Antennas" he sets out to solve
Hallen`s equation for current distribution. On page 239, Kraus writes:
"It is generally assumed that the current distribution of an
infinitesimally thin antenna is sinusoidal, and that the phase is
constant over a 1/2-wavelength interval, changing abruptly by
180-degrees between intervals."

You can take what Kraus says to the bank.

So is Kraus bankrupt by contrary evidence that presumes he meant his
quote to be taken strictly? Even Kraus hedges with "assumed" and he
does not otherwise force the conclusion, does he? Why indeed would he
for such a trivial topic is the more astute observation.

This entire line of argument (distortion) is wholly specious. This
violates most analysis by demanding that a wavelength sizeable element
conform to lumped expectations. The non-linearity is found along the
entire length of the element, not at a point. The characteristic Z
varies by simple geometrical observation - it doesn't take quantum
mechanics to arrive at this obvious conclusion. The ONLY linear
quarterwave antenna is a biconical dipole - that has been established
since the 40s. Even the Cosine distribution is blatant evidence of
non-linearity (try listening to Mozart with an amp that has a cosine
gain curve). An antenna has to be huge (wavelengths) and close (far
less than a wavelength) to the earth before any linearity begins to
arise - this too is historic.

73's
Richard Clark, KB7QHC

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Richard,

Maybe someone can help us here. Linearity is well-defined in
electronics by the law of superposition, and is characterized by
well-known measurements such as harmonic generation, compression point,
and third-order intercept point. I'm assuming antennas must follow the
same law of superposition while transmitting and receiving to be
linear.

It is not clear to me that a nonlinear or even unpredictable current
distribution along a wire antenna produces signals that violate the law
of superposition. Under a strange current distribution the antenna
radiation pattern will certainly distort, but how does that violate the
law of superposition? That is, how can a strong received signal
influence a weak one on an antenna with nonlinear current distribution?

Maybe, like so many other threads in this group, we are discussing
orthogonal concepts.

73,
Glenn AC7ZN

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In article .com,
wrote:

Maybe, like so many other threads in this group, we are discussing
orthogonal concepts.

I believe you're correct.

As I see it, in the *general* sense, linearity refers to a
relationship between two variables, where the relationship is one of

OUT = IN * F + C

where F and C are constants (plus a dimensional factor in many cases).
In other words, it's a straight-line relationship (hence, the name)
between two variables of the same or different dimension.

The sort of "linearity" that people usually refer to in electronics,
involves voltages and currents (vs. one another). A theoretically
perfect resistor, capacitor, or inductor is linear, because (e.g.) the
peak current through it has a strictly linear relationship to the peak
voltage across it.

A semiconductor junction is described as nonlinear, because the
current through it is not related to the voltage across it in a
strictly linear relationship.

The sort of "linearity" which Cecil seems to be referring to (if I
understand what he's written correctly) involves a completely
different sort of relationship. It's not current-vs-voltage, or
voltage-vs-current - it's current-vs-distance.

If I recall correctly, an infinitesimally-short "monopole" has a
current-vs-distance relationship which is close to linear. A
half-wave monopole does not.

Nonlinearities of this sort would have entirely different effects on
an antenna system than nonlinearities of the voltage-vs-current sort.

They're two different beasts entirely.

--
Dave Platt AE6EO
Hosting the Jade Warrior home page: http://www.radagast.org/jade-warrior
I do _not_ wish to receive unsolicited commercial email, and I will
boycott any company which has the gall to send me such ads!

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Richard Harrison wrote:
Tom Donaly, KA6RUH wrote:
"Actually, it`s supposed to be impossible to represent the current
distribution along a dipole using simple mathematical formulas because
integral equations have to be solved that are impervious to any solution
other than numerical approximation."

How many places do you attach to pi?

First, what is linearity? It is the absence of nonlinearity.

Millman and Seely wrote on page 525 of the 1951 edition of "Electronics"
(one of my old textbooks):
"Because of this nonlinear characteristic of the dynamic curve over the
operating range, the wave form of the output wave differs slightly from
that of the grid-exciting-voltage waveshape. Distortion of this type is
called "nonlinear" or "amplitude" distortion.."

All of the antennas I`ve worked with had no noticeable amplitude
distortion. They caused no harmonics or mixing products.

On page 235 of Kraus` 1950 edition of "Antennas" he sets out to solve
Hallen`s equation for current distribution. On page 239, Kraus writes:
"It is generally assumed that the current distribution of an
infinitesimally thin antenna is sinusoidal, and that the phase is
constant over a 1/2-wavelength interval, changing abruptly by
180-degrees between intervals."

You can take what Kraus says to the bank.

Best regards, Richard Harrison, KB5WZI


It certainly is interesting how many supposedly knowledgeable people
can't tell the difference between length and time. Millman and Seely
were writing about cycles per _second_. Kraus was talking about
distribution over _length_. Moreover, read Richard Clark's post
on this subject. Brother!
73,
Tom Donaly, KA6RUH

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Richard Clark wrote:
In other words, the non-linearity shown by the lack of
congruence to the Cosine curve is not a presumption of non-linearity
by the modeler; it is merely reporting an analysis.

You are being fooled by an illusion. Any deviation from
single frequency sinusoidal signals would generate harmonics
which we know doesn't happen. Your "non-linearity" is not
really there. For instance, a decrease in VF may compress
the waveform but that is not non-linearity.
--
73, Cecil http://www.qsl.net/w5dxp

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Tom Donaly wrote:
What he believes is that
since he can't detect any harmonics emanating from a sinusoidally
fed dipole, the current along its length must be a sinusoid.

The non-existence of harmonics is prima facie evidence
that only single frequency sinusoids exist. A properly
functioning antenna system is linear. Any perceived
non-linearity is an illusion.
--
73, Cecil http://www.qsl.net/w5dxp

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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

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Tom Donaly wrote:
People like Cecil, with
home-grown theories, don't ever seem to want things considered in
depth. That's understandable from a psychological standpoint, but
it isn't any help to the rest of us when some of the things the theory
ignores become significant. In the case of antennas, practically
everything is significant.

All of the theories I am quoting were developed long before I was
born. Almost every technical explanation starts out with simple
concepts and proceeds to more complex concepts. For the sake of
teaching and understanding simple concepts, the secondary variables
are often ignored for the time being. Thus, every textbook on
transmission lines starts off with an explanation of lossless lines
with perfectly resistive characteristic impedances even though such
lines don't exist in reality.
--
73, Cecil http://www.qsl.net/w5dxp

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Richard Clark wrote:
How much distortion has to exist before you hear it? As this directly
relates to your quoted selection, are we to believe that distortion
does not exist if you cannot perceive it?

How about: Distortion can be measured.
--
73, Cecil http://www.qsl.net/w5dxp

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Dave Platt wrote:
The sort of "linearity" which Cecil seems to be referring to (if I
understand what he's written correctly) involves a completely
different sort of relationship. It's not current-vs-voltage, or
voltage-vs-current - it's current-vs-distance.

Assuming thin constant diameter wires with a constant Z0 and VF.

If the diameter of the wire changes, or Z0 changes, or VF changes,
the 'K' term in the cos(KX) expression changes. A change in a
constant does NOT produce non-linearity in a linear system. Just
because a wave slows down in a medium with a low VF doesn't mean
that the system has gone non-linear.
--
73, Cecil http://www.qsl.net/w5dxp