Roy, W7EL wrote:
"I`m sure that somewhere in one of your texts you can find the
definition of linear as applied to networks."

Right. From "The Penguin Desk Encyclopedia of Science and Mathematics":

"Linear (algebra) An equation or function of the form ax + by + c = 0
or f(x) = mx +b is called linear because its graph is a line. This has
been generalized to a concept called linear combination, which is the
sum of 2 or more entities with each multiplied by some number (with not
all numbers being 0). Linear combinations of vectors, equations, and
functions are commonly employed."

I think that definition is broad enough to cover the representations I
made in my postings.

Best regards, Richard Harrison, KB5WZI

I can only hope that some of the readers understand.

Roy Lewallen, W7EL

Richard Harrison wrote:
Roy, W7EL wrote:
"I`m sure that somewhere in one of your texts you can find the
definition of linear as applied to networks."

Right. From "The Penguin Desk Encyclopedia of Science and Mathematics":

"Linear (algebra) An equation or function of the form ax + by + c = 0
or f(x) = mx +b is called linear because its graph is a line. This has
been generalized to a concept called linear combination, which is the
sum of 2 or more entities with each multiplied by some number (with not
all numbers being 0). Linear combinations of vectors, equations, and
functions are commonly employed."

I think that definition is broad enough to cover the representations I
made in my postings.

Best regards, Richard Harrison, KB5WZI

Richard Harrison wrote:

Roy, W7EL wrote:
"I`m sure that somewhere in one of your texts you can find the
definition of linear as applied to networks."

Right. From "The Penguin Desk Encyclopedia of Science and Mathematics":

"Linear (algebra) An equation or function of the form ax + by + c = 0
or f(x) = mx +b is called linear because its graph is a line. This has
been generalized to a concept called linear combination, which is the
sum of 2 or more entities with each multiplied by some number (with not
all numbers being 0). Linear combinations of vectors, equations, and
functions are commonly employed."

I think that definition is broad enough to cover the representations I
made in my postings.

Best regards, Richard Harrison, KB5WZI




You're right in a certain mathematical sense, but that definition
isn't correct, as Roy pointed out, in defining superposition.
73,
Tom Donaly, KA6RUH

OK, you guys can stop now... wx is improving and i found something more fun
to play with anyway.... try this site out:

The links don't mail well, but if you go to this link...
http://local.live.com/?v=2&sp=aN.42.....022505_k1ttt_

and then do this....

After the page above displays the road view, in the control pad at the top
left click on 'bird's eye'... then wait for it to redraw. Then click on the
'W' on the compass rose to view toward the west which seems to be the
closest view of my place. Then click on the big set of buildings in that
control panel to zoom in. by this point you won't see the station at all,
but in the 'scratch pad' control on the right side click on the 'k1ttt' link
and it should swing it around and show you a view of my station looking
toward the west. the photo is at least 3 to 4 years old now as you can see
the 6 element 20m and 8 element 15m yagi's still up that have been replaced.

David Robbins K1TTT

web: http://www.k1ttt.net

AR-Cluster node: 145.69MHz or telnet://dxc.k1ttt.net

OK, you guys can stop now... wx is improving and i found something more
fun to play with anyway.... try this site out:

The links don't mail well, but if you go to this link...
http://local.live.com/?v=2&sp=aN.42.....022505_k1ttt_

and then do this....

After the page above displays the road view, in the control pad at the top
left click on 'bird's eye'... then wait for it to redraw. Then click on
the 'W' on the compass rose to view toward the west which seems to be the
closest view of my place. Then click on the big set of buildings in that
control panel to zoom in. by this point you won't see the station at all,
but in the 'scratch pad' control on the right side click on the 'k1ttt'
link and it should swing it around and show you a view of my station
looking toward the west. the photo is at least 3 to 4 years old now as you
can see the 6 element 20m and 8 element 15m yagi's still up that have been
replaced.

David Robbins K1TTT

web: http://www.k1ttt.net

AR-Cluster node: 145.69MHz or telnet://dxc.k1ttt.net

Oh my goodness! The critical qualification and definition has been provided
by Roy.
Roy and Richard then proceeded to nail the subject to the proverbial wall.

It is time to pause in grading exams to remind that analytic geometry and
circuit theory are not the same thing. In circuit theory (and practice) a
circuit/network/or-whatever is linear if, and only if, superposition is
satisfied. If superposition is satisfied, then the circuit in question is
linear.

This concept also has utility in some mechanical structures.

In English, it is not uncommon for a word to have quite different meanings
depending on where it is used. We all know this. Even when discussing
active devices such as BJTs and FETs one finds the word "saturation" used
differently depending on the device.

Obviously, large enough signals applied to any network that appears to be
linear with smaller signals will melt same - letting out the smoke that was
placed therein at the factory. Obviously, there are degrees of linearity.
A footnote is always understood to say: such-and-such network is acceptably
linear for signals larger than A and smaller than B.

... thus ends the lesson.

73, Mac N8TT
--
J. Mc Laughlin; Michigan U.S.A.
Home:
"Roy Lewallen" wrote in message
...
I can only hope that some of the readers understand.

Roy Lewallen, W7EL

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.

73, Mac N8TT

--
J. Mc Laughlin; Michigan U.S.A.
Home:
"Richard Clark" wrote in message
...
On Tue, 23 May 2006 08:55:42 -0500, (Richard
Harrison) wrote:

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

Hi Richard,

Try listening to Mozart with a speaker driven with such a "linear"
gain device. [Some things are so simple, they defy further analysis.]

This, again, goes to the matter of a finely staged distortion trial
with tone-deaf judges.

73's
Richard Clark, KB7QHC

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

Tom, KA6RUH wrote:
"You`re right in a certain mathematical sense, but that definition isn`t
correct as Roy pointed out in defining superposition."

Or in conjugate matching for that matter. The discussion was: Is an
antenna a linear device, meaning does it produce amplitude distortion?

Amplitude distortion comes from a nonlinear relation between imput and
output. It has nothing to do with has the amplitude grown larger or
smaller in the antenna? I think the majority of antennas have an output
which is a reasonable approximation in form to their input. That goes
for frequencies too. The response won`t be the same for all frequencies,
but you`re not likely to find new frequencies on the output of the
antenna that aren`t on its input.

Superposition says that when a number of voltages (distributed in any
manner throughout a linear network) are applied to the network
simultaneously, the current that flows is the sum of the component
currents that would flow if the same currents had acted individually.

As Cecil said, nonlinearity produces new frequencies. Good antennas
don`t do that, superposition or not.

Best regards, Richard Harrison, KB5WZI

On Tue, 23 May 2006 19:21:45 -0500, (Richard
Harrison) wrote:

As Cecil said, nonlinearity produces new frequencies. Good antennas
don`t do that, superposition or not.

Hi Richard,

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.

Saying that this non-linearity must then reveal (of all things) an
amplitude distortion is specious. Demanding that "new frequencies"
must exist AND then saying they must be of such-and-such a magnitude
to so qualify is a hoot.

This is old ground and has not been answered by you or Cecil. Saying
't'ain't so is not debate.

73's
Richard Clark, KB7QHC