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.

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.

Paul Burridge wrote:
On Sun, 7 Sep 2003 18:52:46 +0100, "Kevin Aylward"
wrote:



This
results in one main fact. She chooses a mate, essentially, only on
the basis of good gene stock. She doesn't want a nice person because
this would mean her offspring would also be nice, and thereby do
things not in there own best interest. She wants a "mean" offspring.
That is, treat them mean, keeps them keen The theories great. It
explains quite nicely why women chose those yobbys that beat them up.

Can't agree there. Women are basically genetically obliged to pick the
best mate they can get their hands on, given the limitations imposed
by their own pulling abilities.

By and large, this is not significant. The numbers can be increased by
quality or quantity. A man will have sex pretty much with *any* women,
so long as they're not fat:-). If a women goes up to a man stranger, in
a pub and says, lets go back to my place, its a done deal. There is no
much of a disadvage numbers wise, a man has offspring by every women he
can so he does. On the over hand, a women can not do this. Once she's
pregnant, that's her out of the game for 9 months. The only way she can
get her genes to replicate faster is by choosing better gene stock. This
makes her absolutely choosy.

What they are looking for in every
case is a mate who can give their offspring the best chance of
survival and 'thrival' in this wide, mean world.

I think you have still missed an important point here. Yes, I agree that
there is some truth in this, and this is a pretty obvious analysis, but
it is not that significant. The most important facter is good gene
stock. Its the only factor. She will chose a mate based on what
characteristics the offspring will have. Not what's in her personal best
interest. The body is only a vehicle for the genes. Bodies don't copy
themselves, so cant form a basis for replication, only genes replicate.
If it is the net best interest of the genes, they will sacrifice the
vehicle to enable better success for themselves.

Interestingly enough,
the qualities the male must display to succeed change according to
different ages (historical ages, not biological) and cultures. At
varying times, men have been favoured because of, for example, they're
exceptionally good fighters. Or unusually good hunters... later in
history, we see female preferences based on wealth and status. But in
countries where for idealogical reasons, all people are 'made to be
equal' like the old Soviet Union or the 'old' China, females must pick
according to other criteria such as a gift for literature, music or
art. They're all programmed to do their best for the unborn child,
even if they don't want children at all or are too old to conceive.

But in practice, the single most significant aspect, even today, is
physical appearance. It has to be. Its pretty much universal what is
considered good looking, many studies have been done. Sure, its useful
to have other aspects. A show of wealth, is obviously an indicator that
her offspring may also get this characteristic (ignoring the details of
how for now), but in pracise, you have to be pretty damn weathy if you
want to take Liz Harley to bed.


I don't agree. Reviews mean f'all. Have you actually read all the
"review" on the later editions of Hawking's "Brief history of time".
It make you want to vomit. Sure, his a very clever dude, but he is
ceratyinly not a god.

I didn't say he was. In fact he admitted to wasting much time working
on 'singularities' with Roger Penrose donkey's years ago.

As noted above, it was the selfish gene that revolutionised the
approach to evolution as to the body being a mere vehicle for the
masters, the genes and memes.

Let's just put it down to a matter of personal preference, then.

[not particularly relevant Einstein example snipped]

Oh?


The whole emphases on Darwin is wrong, it is a legacy theory. The
fundamental idea is the Replicator, as such, a "handicap" is just a
specific detail of how some particular Replicators can replicate
better.

I'm not sure what you're driving at here but I don't like the sound of
it.


That's because you didn't see the point of the Einstein example. Go back
and read it again to get the *bigger* picture.

Rubbish. You demonstrably know sweet FA about global economics as
demonstrated in our recent exchanges on the subject where you cut
and run like a scalded cat when faced with cogent arguments from
someone (me) with indisputable expertise in the area.

Nonsense. It was just something that I could not be bothered to
debate. I have little interest in economics, other than how much I
get paid, which concerns me greatly.

LOL! Yeah, whatever. You quit while you were behind. You should have
quit earlier but I think you just about backed out before you
sustained any terminal damage. :-)

Nope. I happen to believe in conservation of energy and momentum. You
views denied this. I look at the bigger picture. I am not familiar with
all the details of economics so I didn't want to get bogged down there.
A general theorem that you cant get blood from a stone doesn't need the
details, but as I said, cant be bothered expanding on it.


If your claiming that Dawkins retracted the basics of Replicators,
then your dreaming. I'll have to see what Miller is specifically
addressing.

I'm suggesting no such thing. I'm simply saying that Dawkins softened
his line of selfishness a good measure from the position you wrongly
(now) attribute to him.

If you mean that we might be able to override the gene's "intentions", I
don't know if what he says is really what he believes, or is an attempt
to appease the masses for politically correct reasons.

The problem is, the only way to override a Replicator, is make a better
one. Unfortunately, the ones we have, have millions of years of a head
start. You try not getting a hard on if naked striper sits on your lap.


I have read a few bits and bobs from creationists who claim that
Dawkins recanted on his evolutionary views. It was all crap, as he
himself explained.

Yes I know. The attempts were laughable.

Well, obviously, you could not refute my argument that selfishness is
inherent. As I said, its a tautology. It can't be contradicted.

Okay, well let's put you this question: if everyone is basically
selfish, why do some people help other people out on newsgroups?

I explained this, the 5 team bunch of skinheads verses the single guy,
although there is a number of factors. The fundermental reason is that
the genes expect a payback. Of course, detrimental characteristics are
still being randamly generated, so some of them are fools. Have you been
to the dawin awards site http://www.darwinawards.com/ ?

In *general*, is it good or bad to gain a respected reputation?

Genes don't know when helping is going to be beneficial or not, they
cant think. They don't know the future. Replication is only based on
probabilities. If you help nobody, what's the probability you will get
help back? One has to look at the numbers from game theory. Give various
traits, e.g helpfulness, punishment, slyness, e.g. tit for tat strategy
etc. The final numbers give what strategies are stable, or drive the
group to extinction.

So, people are helpful to others because, statistically, this strategy
results in net benefit to themselves, statisticly.

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.

Paul Burridge wrote:
On Sun, 7 Sep 2003 18:52:46 +0100, "Kevin Aylward"
wrote:



This
results in one main fact. She chooses a mate, essentially, only on
the basis of good gene stock. She doesn't want a nice person because
this would mean her offspring would also be nice, and thereby do
things not in there own best interest. She wants a "mean" offspring.
That is, treat them mean, keeps them keen The theories great. It
explains quite nicely why women chose those yobbys that beat them up.

Can't agree there. Women are basically genetically obliged to pick the
best mate they can get their hands on, given the limitations imposed
by their own pulling abilities.

By and large, this is not significant. The numbers can be increased by
quality or quantity. A man will have sex pretty much with *any* women,
so long as they're not fat:-). If a women goes up to a man stranger, in
a pub and says, lets go back to my place, its a done deal. There is no
much of a disadvage numbers wise, a man has offspring by every women he
can so he does. On the over hand, a women can not do this. Once she's
pregnant, that's her out of the game for 9 months. The only way she can
get her genes to replicate faster is by choosing better gene stock. This
makes her absolutely choosy.

What they are looking for in every
case is a mate who can give their offspring the best chance of
survival and 'thrival' in this wide, mean world.

I think you have still missed an important point here. Yes, I agree that
there is some truth in this, and this is a pretty obvious analysis, but
it is not that significant. The most important facter is good gene
stock. Its the only factor. She will chose a mate based on what
characteristics the offspring will have. Not what's in her personal best
interest. The body is only a vehicle for the genes. Bodies don't copy
themselves, so cant form a basis for replication, only genes replicate.
If it is the net best interest of the genes, they will sacrifice the
vehicle to enable better success for themselves.

Interestingly enough,
the qualities the male must display to succeed change according to
different ages (historical ages, not biological) and cultures. At
varying times, men have been favoured because of, for example, they're
exceptionally good fighters. Or unusually good hunters... later in
history, we see female preferences based on wealth and status. But in
countries where for idealogical reasons, all people are 'made to be
equal' like the old Soviet Union or the 'old' China, females must pick
according to other criteria such as a gift for literature, music or
art. They're all programmed to do their best for the unborn child,
even if they don't want children at all or are too old to conceive.

But in practice, the single most significant aspect, even today, is
physical appearance. It has to be. Its pretty much universal what is
considered good looking, many studies have been done. Sure, its useful
to have other aspects. A show of wealth, is obviously an indicator that
her offspring may also get this characteristic (ignoring the details of
how for now), but in pracise, you have to be pretty damn weathy if you
want to take Liz Harley to bed.


I don't agree. Reviews mean f'all. Have you actually read all the
"review" on the later editions of Hawking's "Brief history of time".
It make you want to vomit. Sure, his a very clever dude, but he is
ceratyinly not a god.

I didn't say he was. In fact he admitted to wasting much time working
on 'singularities' with Roger Penrose donkey's years ago.

As noted above, it was the selfish gene that revolutionised the
approach to evolution as to the body being a mere vehicle for the
masters, the genes and memes.

Let's just put it down to a matter of personal preference, then.

[not particularly relevant Einstein example snipped]

Oh?


The whole emphases on Darwin is wrong, it is a legacy theory. The
fundamental idea is the Replicator, as such, a "handicap" is just a
specific detail of how some particular Replicators can replicate
better.

I'm not sure what you're driving at here but I don't like the sound of
it.


That's because you didn't see the point of the Einstein example. Go back
and read it again to get the *bigger* picture.

Rubbish. You demonstrably know sweet FA about global economics as
demonstrated in our recent exchanges on the subject where you cut
and run like a scalded cat when faced with cogent arguments from
someone (me) with indisputable expertise in the area.

Nonsense. It was just something that I could not be bothered to
debate. I have little interest in economics, other than how much I
get paid, which concerns me greatly.

LOL! Yeah, whatever. You quit while you were behind. You should have
quit earlier but I think you just about backed out before you
sustained any terminal damage. :-)

Nope. I happen to believe in conservation of energy and momentum. You
views denied this. I look at the bigger picture. I am not familiar with
all the details of economics so I didn't want to get bogged down there.
A general theorem that you cant get blood from a stone doesn't need the
details, but as I said, cant be bothered expanding on it.


If your claiming that Dawkins retracted the basics of Replicators,
then your dreaming. I'll have to see what Miller is specifically
addressing.

I'm suggesting no such thing. I'm simply saying that Dawkins softened
his line of selfishness a good measure from the position you wrongly
(now) attribute to him.

If you mean that we might be able to override the gene's "intentions", I
don't know if what he says is really what he believes, or is an attempt
to appease the masses for politically correct reasons.

The problem is, the only way to override a Replicator, is make a better
one. Unfortunately, the ones we have, have millions of years of a head
start. You try not getting a hard on if naked striper sits on your lap.


I have read a few bits and bobs from creationists who claim that
Dawkins recanted on his evolutionary views. It was all crap, as he
himself explained.

Yes I know. The attempts were laughable.

Well, obviously, you could not refute my argument that selfishness is
inherent. As I said, its a tautology. It can't be contradicted.

Okay, well let's put you this question: if everyone is basically
selfish, why do some people help other people out on newsgroups?

I explained this, the 5 team bunch of skinheads verses the single guy,
although there is a number of factors. The fundermental reason is that
the genes expect a payback. Of course, detrimental characteristics are
still being randamly generated, so some of them are fools. Have you been
to the dawin awards site http://www.darwinawards.com/ ?

In *general*, is it good or bad to gain a respected reputation?

Genes don't know when helping is going to be beneficial or not, they
cant think. They don't know the future. Replication is only based on
probabilities. If you help nobody, what's the probability you will get
help back? One has to look at the numbers from game theory. Give various
traits, e.g helpfulness, punishment, slyness, e.g. tit for tat strategy
etc. The final numbers give what strategies are stable, or drive the
group to extinction.

So, people are helpful to others because, statistically, this strategy
results in net benefit to themselves, statisticly.

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.

gwhite wrote:
Kevin Aylward wrote:

gwhite wrote:

Its that simple. I clearly stated that it was *not* a
definition.

"Linearity can more easily be expressed as: a(f(t)) = f(at)" -- Kevin
Aylward

I think someone is posting under your name. A nasty bit of business
that is.

Linearity can be expressed by this, however, it is not a necessary
condition. I never claimed that it was a complete definition.


It was simply trying to illustrate the concept of constant
gain. You expanding on some trivial minor point to avoid answering
the main issue, to wit, you have failed to disprove my claim on your
class A amplifier.

Class A works just fine in multipliers/modulators

Never said it didn't. However, the class A bit does not account for how
they multiply.

-- "non-linearity"
of circuit elements is not required.

Ho humm. Now for the example that does indeed use non-linearity.

Maybe you can analyze the old
MC1496. That would be enlightening to you.

Yep.

Not at all. You are an completly mistaken. It is abundantly clear that
you don't know the first thing about analogue circuit design. It is
truly amazing and unbelievable that you can be so wrong and not be aware
of it. You are an incompetent.

The MC1496 is a double balanced modulator based on the Gilbert cell
transconductance multiplier. The Gilbert cell multiplier relies on the
exponential relation of collector current to base emitter voltage. That
is, its transconcutane is a function of its emitter current. Its well
understood by all those knowledgeable in the field. to wit:

I = Io.exp(V/Vt)

transconductance gm = dI/dv = d(Io.exp(V/Vt))/dv

gm = Io/Vt.exp(V/Vt)) = Ie/Vt

That is, the gm is a function of Ie.

Since:

Iout = gm.Vin

we have

Iout = Ie/Vt.Vin

That is, Iout is a product of, Ie and Vin. Making Ie a function of
another voltage results in the multiplication of two voltages, i.e. a
modulator.

How you can make such daft claims and not be embarrassed shows greate
stamina, I must say.


But more important and
more simple (it will save you loads of time), just apply *the*
linearity test for

h(t)
x(t) - y(t).

You still haveny cottoned on the fact that you wily nilly apply
definitions you no hope of understanding.


The notion that y=x^2 is a non-linear equation is
universally accepted by anyone who has done even the slightest bit of
theory on basic algebraic equations. It does not require any
qualification in the slightest.

No ****, by why are you rambling on and on about it?

Because you don't understand it.


Show me one, and I mean just one, that
declares y=x^2 a linear equation.

That is clever -- you want me to "declare" something is true that I've
made no reference to.

You have. See above. You claimed the Gilbert cell did not rely on
non-linearity. Jesus wept again. Your so out to lunch on this that its
unreal. Look, own up your just trolling aren't you.

You are quite the inventor. Face it: you had
an incorrect notion about linearity.

Dream on. You have been soundly proven wrong, and why you are wrong.

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.

gwhite wrote:
Kevin Aylward wrote:

gwhite wrote:

Its that simple. I clearly stated that it was *not* a
definition.

"Linearity can more easily be expressed as: a(f(t)) = f(at)" -- Kevin
Aylward

I think someone is posting under your name. A nasty bit of business
that is.

Linearity can be expressed by this, however, it is not a necessary
condition. I never claimed that it was a complete definition.


It was simply trying to illustrate the concept of constant
gain. You expanding on some trivial minor point to avoid answering
the main issue, to wit, you have failed to disprove my claim on your
class A amplifier.

Class A works just fine in multipliers/modulators

Never said it didn't. However, the class A bit does not account for how
they multiply.

-- "non-linearity"
of circuit elements is not required.

Ho humm. Now for the example that does indeed use non-linearity.

Maybe you can analyze the old
MC1496. That would be enlightening to you.

Yep.

Not at all. You are an completly mistaken. It is abundantly clear that
you don't know the first thing about analogue circuit design. It is
truly amazing and unbelievable that you can be so wrong and not be aware
of it. You are an incompetent.

The MC1496 is a double balanced modulator based on the Gilbert cell
transconductance multiplier. The Gilbert cell multiplier relies on the
exponential relation of collector current to base emitter voltage. That
is, its transconcutane is a function of its emitter current. Its well
understood by all those knowledgeable in the field. to wit:

I = Io.exp(V/Vt)

transconductance gm = dI/dv = d(Io.exp(V/Vt))/dv

gm = Io/Vt.exp(V/Vt)) = Ie/Vt

That is, the gm is a function of Ie.

Since:

Iout = gm.Vin

we have

Iout = Ie/Vt.Vin

That is, Iout is a product of, Ie and Vin. Making Ie a function of
another voltage results in the multiplication of two voltages, i.e. a
modulator.

How you can make such daft claims and not be embarrassed shows greate
stamina, I must say.


But more important and
more simple (it will save you loads of time), just apply *the*
linearity test for

h(t)
x(t) - y(t).

You still haveny cottoned on the fact that you wily nilly apply
definitions you no hope of understanding.


The notion that y=x^2 is a non-linear equation is
universally accepted by anyone who has done even the slightest bit of
theory on basic algebraic equations. It does not require any
qualification in the slightest.

No ****, by why are you rambling on and on about it?

Because you don't understand it.


Show me one, and I mean just one, that
declares y=x^2 a linear equation.

That is clever -- you want me to "declare" something is true that I've
made no reference to.

You have. See above. You claimed the Gilbert cell did not rely on
non-linearity. Jesus wept again. Your so out to lunch on this that its
unreal. Look, own up your just trolling aren't you.

You are quite the inventor. Face it: you had
an incorrect notion about linearity.

Dream on. You have been soundly proven wrong, and why you are wrong.

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.

gwhite wrote:
Frank Raffaeli wrote:

gwhite wrote in message
... [snipped long diatribes]

Dude, you are responding to one of the shorter messages.

Class A works just fine in multipliers/modulators --
"non-linearity" of circuit elements is not required. Maybe you can
analyze the old MC1496. That would be enlightening to you. But
more important and more simple (it will save you loads of time),
just apply *the* linearity test

[snip]
Hmmm .... you may be mistaking the (sometimes linear) current
steering effect for the mechanism within the transistor that makes
current steering possible: the relationship between gm and Ic ... or
from another POV, the change in rbb with respect to bias current.
These effects are non-linear.


Non-linearity is *not* required to create DSB-AM out of
transconductance type multipliers like the gilbert cell. In fact,
*non-linearity is specifically something that designers hope to
minimize* -- just like in any linear device. The standard linear
approximation practice ensues: that is, the taylor expansion of
exp(x) is done and the linear term is the desired one and *it is all
that is required or wanted for this linear multiplier*.

Ahh... now I see where the confusion is, and I did already address this
by my comment on the non availability of real, linear voltage controlled
resisters. I stated that in principle, one might be able to find a
device that was strictly linear in order to achieve modulation. I also
stated that such devices do not appear to exist, such that in practise,
one generally has to use a non-linear device to achieve multiplication.

It should go without comment that when one analyses the simple
transistor multiplier that one only selects the first order linear term,
and that this is term that generates the multiplication. This is
trivially obvious, and was what I showed in my original analysis, gm is
inherently a small signal property. Indeed, as this is only valid for
small signals, more complex multipliers log the input signal so that in
conjunction with the exponential relation results in perfect
multiplication at all signal levels, originally due to Gilbert I might
add.

This confusion here appears to me to be one of semantics or x-wires, as
is often the case on strongly held, but oppositely apposed views. gwhite
claims that you don't inherently require a non-linear device to achieve
multiplication, I claim that all practical devices have a non-linear
transfer function, and it is this transfer function that results in
multiplication. I don't believe we are arguing about the same point. I
have nothing more to say on this. I have better things to do.

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.

gwhite wrote:
Frank Raffaeli wrote:

gwhite wrote in message
... [snipped long diatribes]

Dude, you are responding to one of the shorter messages.

Class A works just fine in multipliers/modulators --
"non-linearity" of circuit elements is not required. Maybe you can
analyze the old MC1496. That would be enlightening to you. But
more important and more simple (it will save you loads of time),
just apply *the* linearity test

[snip]
Hmmm .... you may be mistaking the (sometimes linear) current
steering effect for the mechanism within the transistor that makes
current steering possible: the relationship between gm and Ic ... or
from another POV, the change in rbb with respect to bias current.
These effects are non-linear.


Non-linearity is *not* required to create DSB-AM out of
transconductance type multipliers like the gilbert cell. In fact,
*non-linearity is specifically something that designers hope to
minimize* -- just like in any linear device. The standard linear
approximation practice ensues: that is, the taylor expansion of
exp(x) is done and the linear term is the desired one and *it is all
that is required or wanted for this linear multiplier*.

Ahh... now I see where the confusion is, and I did already address this
by my comment on the non availability of real, linear voltage controlled
resisters. I stated that in principle, one might be able to find a
device that was strictly linear in order to achieve modulation. I also
stated that such devices do not appear to exist, such that in practise,
one generally has to use a non-linear device to achieve multiplication.

It should go without comment that when one analyses the simple
transistor multiplier that one only selects the first order linear term,
and that this is term that generates the multiplication. This is
trivially obvious, and was what I showed in my original analysis, gm is
inherently a small signal property. Indeed, as this is only valid for
small signals, more complex multipliers log the input signal so that in
conjunction with the exponential relation results in perfect
multiplication at all signal levels, originally due to Gilbert I might
add.

This confusion here appears to me to be one of semantics or x-wires, as
is often the case on strongly held, but oppositely apposed views. gwhite
claims that you don't inherently require a non-linear device to achieve
multiplication, I claim that all practical devices have a non-linear
transfer function, and it is this transfer function that results in
multiplication. I don't believe we are arguing about the same point. I
have nothing more to say on this. I have better things to do.

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.

Kevin Aylward wrote:
gwhite wrote:

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

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.

A light dependant resistor. One input drives a LED via a linearizer
to compensate for LDR non-linearity. The LDR resistance is unaffected
by the voltage across it. Therefore, the resulting current
Io=f(V1,V2)= k.V1*V2 (4-quadrant multiplier or compensated gilbert cell)

The circuit output is *superposition linear* relative to each input.
dIo/dV1=k.V2, dIo/dV2=k.V1 (partial derivatives). In mixer operation,
Io=f(Vin,Vosc). Vosc is an independant time-varying signal.
Therefore, Io=f(Vin,Vosc(t)) or Io(t)=g(Vin,t). Because Io vs Vin
is linear (4-quad multiplier), then dIo/dVin= g'(t) ie: a function
of time only. This is the definition of a linear time-varying
circuit.

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.

An ideal multiplier is considered nonlinear with respect to a certain
signal if a component of that signal is applied to *both* inputs
simultaneously. Then:

Io=k.(V1+a.V2)(a.V1+V2)= k.( aV1^2 + a.V2^2 + (1+a^2).V1.V2 )

Kevin Aylward wrote:
gwhite wrote:

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

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.

A light dependant resistor. One input drives a LED via a linearizer
to compensate for LDR non-linearity. The LDR resistance is unaffected
by the voltage across it. Therefore, the resulting current
Io=f(V1,V2)= k.V1*V2 (4-quadrant multiplier or compensated gilbert cell)

The circuit output is *superposition linear* relative to each input.
dIo/dV1=k.V2, dIo/dV2=k.V1 (partial derivatives). In mixer operation,
Io=f(Vin,Vosc). Vosc is an independant time-varying signal.
Therefore, Io=f(Vin,Vosc(t)) or Io(t)=g(Vin,t). Because Io vs Vin
is linear (4-quad multiplier), then dIo/dVin= g'(t) ie: a function
of time only. This is the definition of a linear time-varying
circuit.

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.

An ideal multiplier is considered nonlinear with respect to a certain
signal if a component of that signal is applied to *both* inputs
simultaneously. Then:

Io=k.(V1+a.V2)(a.V1+V2)= k.( aV1^2 + a.V2^2 + (1+a^2).V1.V2 )