Dear Richard:

Last week's lab job in both Electronics I and II (at different levels)
explored just this issue.
How great it is to have really good scopes and a spectrum analyzer in a
student tab.

73 Mac N8TT

--
J. Mc Laughlin; Michigan U.S.A.
Home:
"Richard Clark" wrote in message
...
On Tue, 23 May 2006 19:11:00 -0400, "J. Mc Laughlin"
wrote:

Dear Richard:

I have had occasion to note to students that some of what they call music
would not be noticeably modified by being amplified by a amplifier having
a
great deal of distortion.

Your point is right on target.

Hi Mac,

My point may have been on target, but the specifics left an escape for
those quick enough to pick up on it. In fact, I would speculate that
most audio (as do RF) amplifiers exhibit the gain characteristic of
f(x) = y = mx + b
and this is called class AB. When you build an amp employing two of
them in a push-pull configuration the constants b negate each other
and the 2mx remains.

Of course, the push-pull configuration is built to nullify the
distortion of this "linear" curve.

The single power supply Op Amp also suffers from
f(x) = y = mx + b
with the output floating at half the supply voltage - this has got to
be an application killer if it goes straight to the speakers without
removing the b with a capacitor.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
Appeals of authority that are pegged to Cecil are like trying to tread
water with a concrete life preserver. Your logic is blighted by a
forced conclusion that has nothing to do with the obvious observation
that antennas, as transmission lines, are quite evidently non-linear
in their characteristic Z. This has been demonstrated and is historic
from sources that even Terman's accepts.

There exist transmission lines with a changing Z0 along their
lengths. Those transmission lines are linear systems.
--
73, Cecil http://www.qsl.net/w5dxp

Richard Clark wrote:
"Demanding that "new frequencies" must exist AND then saying that they
must be of such-and-such a magnitude to qualify is a hoot."

Glad you got a kick out of that. It is not original.

In analog microwave systems, often an baseband intermod monitor is used
to alarm the operator that nonlinearity has arrived in his system. New
frequencies have appeared and have reached a preset arbitrary amplitude
sufficient to trigger an alarm. Nothing is perfect so there will always
be some intermod. This requires setting a level of these intermod
products which will trigger the alarm. This is a standard procedure.

Best regards, Richard Harrison, KB5WZI

On Tue, 23 May 2006 23:01:52 -0500, (Richard
Harrison) wrote:

Richard Clark wrote:
"Demanding that "new frequencies" must exist AND then saying that they
must be of such-and-such a magnitude to qualify is a hoot."

Glad you got a kick out of that. It is not original.


Hi Richard,

All that was missing from your response was the chuckle, and the
number at which distortion begins.

How is it if you are not laughing, that neither are you illuminating
to this specific point that is presumable a serious issue? Such a
shortfall doesn't inspire much confidence in your logic, which perhaps
sank with that concrete life jacket.

C'mon, is 10% distortion to be mandated as linear, and 11% distortion
non-linear? Need we push this to Cecil's Limit of perception - ±59%?

Choose your own numbers, or find a true authority to quote a
quantitative response.

73's
Richard Clark, KB7QHC

Richard Clark wrote:
"Choose your own numbers, or find an authority to quote a quantitave
response."

If you can`t detect it, it might as well not exist. If you do detect it,
it`s up to you to correct it or not.

How many antennas have troubled you with new frequencies?

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:
How many antennas have troubled you with new frequencies?

Half a century ago, I installed a ceramic capacitor
across the feedpoint of my dipole to change the
resonant frequency. I'm sure it generated some new
frequencies when it blew up and caught on fire. :-)
--
73, Cecil http://www.qsl.net/w5dxp

Roy Lewallen wrote:
I'm sure that somewhere in one of your texts you can find the definition
of linear as applied to networks. Once you do, though, a little thought
is required to discover that y = mx + b doesn't satisfy the criteria for
network linearity.

To be linear, a network has to satisfy superposition. This means that:

If y1 is the response to excitation x1 and y2 is the response to
excitation x2, then the response to x1 + x2 must be y1 + y2.

Let's try that with your function.

The response to x1 is:

y(x1) = mx1 + b

The response to x2 is:

y(x2) = mx2 + b

The sum of y(x1) and y(x2) is:

y(x1) + y(x2) = m(x1 + x2) + 2b

But response to x1 + x2 is:

y(x1 + x2) = m(x1 + x2) + b

These are not equal as they must be to satisfy superposition and
therefore the requirements for linearity.

Roy Lewallen, W7EL

Richard Harrison wrote:
Roy Lewallen, W7EL wrote:
"But of course you realize that the function y = mx + b doesn`t meet the
requirements of a linear function when applied to network theory."

Works for me.

Linear means the graph of the function is a straight line.

f(x) = y = mx + b is called linear because its graph is a straight line.

A straight line is the shortest distance between two points.

In y = mx + b, m is a constant determining the slope of the line. x is
is the independent variable. b is the offset or point along the x-axis
where the line crosses.

y then is a linear function of x because its slope is always mx, but
displaced in the x-direction by a constant value, namely b.

y is linear the same as IR is linear, or by substitution, E is linear in
Ohm`s law where E=IR. For any value of I, voltage = IR and the graph of
I versus E is a straight line with a slope equal to R.

Resistance is a common factor in network theory.

Best regards, Richard Harrison, KB5WZI

Not that it means anything, but the linearity requirement is met when
b = 0, which, of course, is a subset of the family of equations of the
form y = mx + b.

73,

Chuck
NT3G

On Wed, 24 May 2006 09:00:52 -0500, (Richard
Harrison) wrote:

Richard Clark wrote:
"Choose your own numbers, or find an authority to quote a quantitave
response."

If you can`t detect it, it might as well not exist. If you do detect it,
it`s up to you to correct it or not.

Hi Richard,

So the long and short of it is that you cannot supply us with any
quantifiable information and that you rely solely on impression.

Your explanation sounds like you are practicing psychiatry, not
technology. Given the repetition of the same vague answers would give
rise to the commonplace observation:
the definition of insanity is doing the same thing
over and over, expecting a new outcome.

73's
Richard Clark, KB7QHC

A good target number for antenna linearity would be one that does not
limit system dynamic range. Our best receivers have a dynamic range of
around 120 dB as measured by the minimum discernable signal on the low
end, and the point where two-tone third order distortion products are
detectable on the high end.

140 dB seems reasonable for an antenna and would theoretically be
measured the same way as receiver dynamic range, though setting up a
noise-free environment, and coupling large distortion-free signals to a
test antenna is a challenge, and is probably one reason we don't see
these measurements. The other reason is that there is good evidence
that a properly built antenna does not limit system dynamic range.
That is, it is very linear in the superposition sense.

By the way, generating new frequencies is not necessarily a violation
of superposition (though it usually is). Consider a system undergoing
a constant Doppler shift.

73,
Glenn AC7ZN

Richard Clark wrote:
"Your explanation sounds like you are practicing psychaitry, not
technoligy."

I think quantification is valuable if the measured value is accurate and
if the value makes a difference.

Antennas are used with transmitters of megawatts of power. These have
limitations by regulations on maximum noise and harmonic content. It
depends on the jurisdiction, but maximum noise and distortion must be at
least 50 dB below the fully modulated level in some locales. I`ve often
used the H.P. noise and distortion analyzer to measure off the air to be
sure we complied with the regulation. It never occurred to me that our
antenna system had a part in noise and distortion production. I expected
curvature in a tube`s characteristics or a failed component to cause a
rise in noise and distortion. Not once do I recall our antenna system
causing distortion anywhere except in the edges of pattern nulls.*This
is normal.

Receiving antennas on the other hand deliver a satisfactory signal
having only microwatts of power. As one responder noted the dynamic
range is enormous. This is not really an issue for concern among
amateurs. Antennas are in general distortion free.

Best regards, RIchard Harrison, KB5WZI