gwhite wrote:
Kevin Aylward wrote:



It is that simple.

Nope. Its not. Linearity has many definitions.

It doesn't have "many definitions" when it comes to the EE profession.
The one definition is wholly consistant across academic texts --
without known contradiction. Everyone who took courses like
Circuits, Fields and Waves, and on and on, also took a Signals and
Systems (or similar under a different name) course. That some, such
as you for example, didn't learn or understand the definition is
notwithstanding.

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.

It is useful to the extent modulation is a linear operation produced
by devices such as gilbert cells biased to Class-A.

Look, you don't even realise that you are using "linear" here in a
completely different sense then one applies it to an equation.

What part of "I agree, that a modulator can be described as a linear
process" do you have trouble with.?

What part of "A modulater usually achives its function by using a
non-linear relation between input voltge/current to output
voltage/current do you have trouble with.?

In one case "linear" is being applied as a property of system as a
whole, in the other it is being applied as a property to an individual
component of system.

Both statements are correct, in their given contest, but they are saying
"different" things.

The issue here is that you have parrot read something from a book, and
then go applying willy nilly it without even the slightest idea of when
it is applicable. Non of the standard references suggest that non-linear
equations are linear. This is daft. There are addressing a different
matter entirely. I have already explained what the distinction is, you
have failed to understand, the point, and I doubt never will.

It is very useful
definition: for example, high data rate modern digital communications
systems routinely utilize linear modulation/demodulation.

Of course its useful, assuming you are competent enough to know when it
can be applied.


It doesn't even matter if the upper transistors in the gilbert cells
are driven to the switch mode (switch mode is not a requirement;
class-A will do) by the LO. It is still linear modulation.

I don't disagree, never claimed otherwise. This is a diffent use of the
word linear. However, it achieves its "linear" modulation by non-linear
means, which you claim it doesn't.


This system is linear:

{sniped teaching granny to suck eggs drivial}


Do you know why?

Yes. I already explained it. You snipped it in my last post.

Jesus wept dude. This is bloody ridiculous. Look sonny boy, snipping my
detailed explanation of why your modulator can be classed as a linear
system, in the given context, shows you for the liar that you are. You
don't impress anyone by attempting to prove a result, you have been
informed at least twice that, is trivial, and that I had already agreed
with that result, in that particular context.


I care about
linearity as understood in the solution of the non-linear
differential equations used in Spice.

Like I said early on: you can make the answer come out however you
want if you are permitted to make up the rules and change them as you
play.

The rules have not been changed. Unfortunately you are too incompetent
to know when to apply the relevant rules.

Show me one Signals, Systems, and Communications text that declares
y=x^2 is a linear equation.

What part of "apples" and "fishnet stockings" did you have trouble with?


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.

It is the definition for the EE profession.

Its apparent you know f'all about definitions in either mathematics or
electronics, nor how to apply them.


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.

That "definition" is incorrect, as has been pointed out already.

It is not, as has been pointed out to you already. proof:

1 Go to *any* and *all* main component vendors web site, e.g. TI, Analog
Devices, Maxim, LT, National, etc

2 Look at their dat sheets and app notes on A/D D/A converters
3 Note the use of FFT testing for linearity.
4 Note how they *all* declare the linearity of A/D D/A by the level of
spurious frequencies

*This* is the definitin that is *actually* uesd in the EE profession.
Its the way it is, and no amount of your huffing and puffing will change
what is standard practise. All you have done here is show that you have
not got a clue on what is standard practise in electronic engineer. Your
words mean nothing

The reality is, is that you are simple trying to hide you failure to
show that your class A amplifier cannot achieve modulation without using
the non-linear relation of input voltage to current. Its as plain as
day.

Produce you proof of Vo(t)= Vi(t).(1+a.sin(wt)) or shut the f'ck up.


I know all about your definition. I dont disagree that it is a valid
definition in some contexts.

It is the definition for the EE context.

Not in the detailed design of electronic circuits it isn't.

If you want an LTI system,
then so be it.

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 is not a matter of a mathematician's characterization of equations.
It is the EE characterization, and this is largely an EE forum. If
you are a mathematician and not an EE, then I can see why you would
believe what you do.

Sorry mate, what part of "there are 100,000's of EE's out there using
Spice, all on the understanding that the equations of electronic design
are non-linear" do you fail to undrstand"? Your a right blooody joke.

You particular Mickey mouse, comic book understanding of what
constitutes an acceptable definition in EE is irrelevant. We real
practicing design engineers don't care about you erroneous waffle.
Secondly, there is not a hope in hell that the authors of your quoted
references will agree with your gross distortion of their books
contents. You have not the slightest ability to apply such knowledge.
Your on you own.


You arnt wrong in this thread because of you particular claim of
linearity.

It isn't "my claim."

It is your claim. No competent author will claim y=x^2 is a linear
equation. Get real.

It is the standard definition for EE's.

As I explained above, complete an utter nonsense. You haven't the
slightest idea of what is standard practise in electronic engineering. I
have been an analogue designer for over 20 years, and no one I have met
uses your suggestion in the design of circuits. Your definition is more
appropriate to complete system design, then discrete component design.

That
some EE's didn't quite "get it" is notwithstanding.

Indeed they dont.

You are simple too dense, are are too much of a coward to admit your
wrong. I explained in detail the two diffent comcepts of lineararity.


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.

Your definition is not the EE definition.

Yes is is. I don't know one competent EE who declares that the
transistor equation is a linear equation.

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.