gwhite wrote:
Kevin Aylward wrote:

Kevin Aylward wrote:
gwhite wrote:
Kevin Aylward wrote:

In summary, there are differing concepts of what linearity is being
understood to mean in the real world.


No again.

No right again.

Those who are confused about it, and can't admit they are
simply wrong about what amounts to a widely accepted definitional
matter, simply take refuge by obscuring
the basics with a bunch of
junk similar to:

"therefore

Vo = 40.Vc.Vi/Re."


Oh dear..oh dear...You claimed that the class A amp was a modulator an
achieved this modulation by way of linear means, you fail to present
your proof of this claim, and then spout of with mathematical waffle,
and claim that I am being obscure?

I clearly showed how the class A amp achieved modulation based on the
non-linear relation of emitter current verses base emitter voltage. The
fact that you have failed to give an alternative mathematically proof
indicates quite clearly that you ****ing in the wind.

Present you argument of exactly how your claim is correct, or retract
you claim.


The simple fact is you are wrong in thinking you can all of the sudden
make up your own definition of linearity, or carry forward without
challenge the mistaken definition of others.

Absolute crap. Show me one respectable math reference that says if
y=exp(x), that y is a linear function of x.

You were right about one
thing: this matter of linearity is pretty basic.

Indeed it is.

You missed it; you
are wrong, that is no big deal.

Indeed its not. My SuperSpice works quite nicely based on the well known
theory of the solution of non-linear differential equations.


The silly part was when you decided
to be condescending about it, for in most practical matters strict
linearity doesn't matter a lot -- most people know what they are
doing well enough such that the accepted definition of linearity is
not explicitly referred to.

I don't have time tonight to provide cited work (I have one from Lahti
that will be particularly useful for this discussion), since it takes
scanning and OCR time and then patch up -- I will do so soon though.
In short, you believe "non-linearity" is *required* for modulators;

Show me one real practical example that does not use a device with a
functional relation between input and output voltage/current that is
linear, as I defined above. As did note as an after thought, it may be
possible in principle, for example, maybe one could construct a true,
linear with voltage, voltage controlled resistor. However, I am not
aware of such magic devices.

The physical reality is that it is not possible. Produce one and I will
retract my claim.

that is incorrect. You confuse the time-invariance property with the
linearity property. You believe LTI systems are the *only* linear
systems -- they are not according to the widely accepted and published
definition of linearity.

No. Linearity is widely understood to have many definitions. I have
explained some of these already.

It is that simple.

Nope. Its not. Linearity has many definitions. In the context of
analogue design, linearity is defined based on where the is a non
straight line between input and output. The whole subject of non-linear
differential equations in spice is based on this concept.

I gave you an example
and worked the solution for you, but still you resist.

Look, I have no problem with your example of a particular definition of
linearity. I already explained how such an example is meaningless in
analogue design by giving an example.

A mathematical definition only has meaning if it is useful when it is
applied. In analogue design this definition is useless, so it is not
used.


You nor anyone else need take my word for it: it is in *all* the
Signals, Systems, and Communications texts I've ever opened up -- they
are wholly consistant with each other; check for yourself.

I don't care a toss about and communication texts. I care about
linearity as understood in the solution of the non-linear differential
equations used in Spice. I suggest that you read some of the many papers
on the solution of such equations.

Look, I don't claim that the particular definition of linearity that you
presence is "wrong" in principle. It is a very well known definition.
However, it is one of many, and is simple not applicable in this
context.

Your
"definition" is not in any of them (af(t) = f(at)???).

I did not say that this was a definition. This was just thrown in as
side line, and I said as much. This was, to all intents and purposes, a
typo. I was meaning to refer to a simple constant gain transfer
function. I clearly said that linearity, as defined in analogue design,
is essentially defined by the absence of any frequencies in the output
not present in the input.

So I feel
justified in simply saying you are flatly wrong.

No. You is you. You have singularly failed to show how your class a amp
is a modulator without using a non-linear relation between input
voltage/current to output voltage/current. If you claim that y=exp(x) is
a linear relation between x an y, further debate is pointless. You don't
the first thing about math.

If you could at
least post a citation from a text that has your definition and a
worked mathematical problem/solution (no "Circuits" junk), then at
least we could say it was all a grand misunderstanding.


www.google.com "nonlinear equations"

www.google.com "nonlinear differential equations" 22,000 hits.

You problem is that you are trying to argue a different point and simple
don't see it. You were off on a roll trying to impress people which
mathematical technicalities that are simple irrelevant in the context of
this original discussion. In short, you are a smart arse.


I must confess here I made a small error.

What wasn't small is your reaction to your "small error." All that
"pretentious drivel" wasn't so pretentious given the fact it is *basic
stuff* that most who've taken the appropriate classes already know

I know all about your definition. I dont disagree that it is a valid
definition in some contexts. However, it is not applicable to electronic
circuit design that is based on the solution of non-linear differential
equations, with the "non-linear" term having a universally accepted
meaning by the 10,000s of mathematician who actually study such
equations.


(it
was a couple definitions and an application using a couple simple trig
identities and no more really).

So basic that you can stand there and declare that:

Y=x^2

is a linear equation. Yeah...LOL. get real.

The meat:

You arnt wrong in this thread because of you particular claim of
linearity. You are wrong because the fundamental claim that you made was
that your class A amp was a modulator that did not rely on the
non-linear transfer function of the emitter current verses Vbe. You have
absolutely failed to explain any exact *details* to support your claim.
That is, show me a specific analysis of the amplifier, without the
irrelevant mathematical waffle, that shows that:

Vo = V(t)(1+ a.sin(wt))

I will accept the argument that you simply misunderstood my, very common
definition of linearity, i.e. y=x^2 is a non-linear equation relation x
to y in *any* mathematical book you care to name, with a linearity
definition more appropriate to general systems analysis.

In closing:

The real reason for this disagreement is that you are talking apples and
I am talking fish net stockings. You are applying the term linearity in
a completely different sense than the one I am using. Both are valid in
principle, and are indeed well accepted, under their appropriate
conditions. The issue however, is that I have made an effort to actually
explain in other posts, what the distinction is, but you are simple too
closed minded or too stupid to understand. In this particular case,
modulation is, in practise, universally achieved by a non-linear
transfer function. That is y=f(x) is non-linear as defined in any math
text book you care to name. Its simple not debatable. However, applying
signals to such a transfer function, can result in the condition, that
given that a certain output is required, non-linearly related to the
input in the strict sense, this output is linearly related to the input
signals. That is, if a certain input gives an output, the sum of two
inputs, give the same output as the individual output sums. In this
sense it may be said to be linear. That is the wanted summed output is
the wanted output of the individual inputs. In one case the term
linearity is being applied to the fact that the output is not a direct
linear function of the input, in the other case, the term linearity is
being applied to the fact the wanted output is is a linear function of
the input sums. That is, in one case, the term linearity is being
applied to the specifics of a system part, where as in the second case
linearity is being applied to a system wide property. What seems to
defies rational belief, is that you seem totally oblivious to the fact
that the term linearity is being applied to two completely different
aspects of a system, and cant be directly compared as to which one is
more valid then another.

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.