RadioBanter - RF amps: tuned load in Class A?

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Don Pearce

September 1st 03 02:24 PM

RF amps: tuned load in Class A?

On Mon, 01 Sep 2003 14:16:51 +0100, Paul Burridge
wrote:

Is a tuned load (tank circuit) a viable load for an RF amplifier
operating in class A? Or is this type of load only really suitable for
class C?

Of course you can use a tuned load with class A. But the nice thing
about a tuned load is that you don't *have* to use class A to achieve
a clean output. Of course, if you are using an amplitude modulated
signal, then you will need class A.

d

_____________________________

http://www.pearce.uk.com

Don Pearce

September 1st 03 02:24 PM

Kevin Aylward

September 1st 03 04:02 PM

Don Pearce wrote:
On Mon, 01 Sep 2003 14:16:51 +0100, Paul Burridge
wrote:

Is a tuned load (tank circuit) a viable load for an RF amplifier
operating in class A? Or is this type of load only really suitable
for class C?

Of course you can use a tuned load with class A. But the nice thing
about a tuned load is that you don't *have* to use class A to achieve
a clean output. Of course, if you are using an amplitude modulated
signal, then you will need class A.

That is, if the input signal is already AM, you need a class A or linear
amplifier. If the AM is to be done at that stage itself, then its the
class c non-linear bit that makes the multiplication modulation work.

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

September 1st 03 04:02 PM

Kevin Aylward

September 1st 03 09:24 PM

Don Pearce wrote:
On Mon, 1 Sep 2003 16:02:24 +0100, "Kevin Aylward"
wrote:

Don Pearce wrote:
On Mon, 01 Sep 2003 14:16:51 +0100, Paul Burridge
wrote:

Is a tuned load (tank circuit) a viable load for an RF amplifier
operating in class A? Or is this type of load only really suitable
for class C?

Of course you can use a tuned load with class A. But the nice thing
about a tuned load is that you don't *have* to use class A to
achieve a clean output. Of course, if you are using an amplitude
modulated signal, then you will need class A.

That is, if the input signal is already AM, you need a class A or
linear amplifier. If the AM is to be done at that stage itself, then
its the class c non-linear bit that makes the multiplication
modulation work.

True - I was considering only the "carrying the signal" case. Anode
modulation of a PA is a different matter.

Yes, I know you knew, I was just tiding up the description a bit for
others.

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

September 1st 03 09:24 PM

Ian Buckner

September 2nd 03 09:30 AM

"Kevin Aylward" wrote in message
...
Don Pearce wrote:
snip
True - I was considering only the "carrying the signal" case.
Anode
modulation of a PA is a different matter.

Yes, I know you knew, I was just tiding up the description a bit for
others.

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.

But did Don know you knew he knew?

Regards
Ian

;-)

Ian Buckner

September 2nd 03 09:30 AM

Don Pearce

September 2nd 03 09:51 AM

On Tue, 2 Sep 2003 09:30:38 +0100, "Ian Buckner"
wrote:

"Kevin Aylward" wrote in message
...
Don Pearce wrote:
snip
True - I was considering only the "carrying the signal" case.
Anode
modulation of a PA is a different matter.

Yes, I know you knew, I was just tiding up the description a bit for
others.

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.

But did Don know you knew he knew?

Regards
Ian

;-)
I had a suspicion that he had an inkling that I might have known that he had a fair idea that I may have had a rough idea.

d

_____________________________

http://www.pearce.uk.com

Don Pearce

September 2nd 03 09:51 AM

Kevin Aylward

September 4th 03 05:19 PM

gwhite wrote:
Kevin Aylward wrote:

Don Pearce wrote:
On Mon, 01 Sep 2003 14:16:51 +0100, Paul Burridge
wrote:

Is a tuned load (tank circuit) a viable load for an RF amplifier
operating in class A? Or is this type of load only really suitable
for class C?

Of course you can use a tuned load with class A. But the nice thing
about a tuned load is that you don't *have* to use class A to
achieve a clean output. Of course, if you are using an amplitude
modulated signal, then you will need class A.

That's what receivers would use since power consumption doesn't matter
much. It would be true for low level TX'er stages too, again because
of power consumption. But for things like "Ham linears" it is not
necessarily true.

That is, if the input signal is already AM, you need a class A or
linear amplifier.

Let's be specific regarding the your word "linear" since "or" implies
something else other than class-A may be possible.

Yes.

Single-ended
"linear" narrow band amps may be biased class-B if the tank has a high
enough Q. The missing half cycle is restored by the so-called
"flywheel effect." In practice deep AB is also used.

If the AM is to be done at that stage itself, then its the
class c non-linear bit that makes the multiplication modulation work.

No.

No. Its Yes. Non-linear action generates the multiplication products. I
was not drawing any real distinction between class c and b in this
context. The practical difference is minimal. They both do not amplifier
the waveform in a linear manner. I was not meaning to infer that it was
an "only" c. I was referring to the fact that you need at least some
method that generates non linarity.

It can be done with class-A or class-B since the assumption is
that the amp will be driven (or nearly so) to the rails by the carrier
alone.

I agree, this is another method of generating x-product multiplication
terms. However, arguable, a class A amplifier is not really a class A
amplifier if it is driven to saturation. Its a really a switching amp
or, a pulse amplitude modulator if its rails are varying.

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

September 4th 03 05:19 PM

gwhite

September 5th 03 01:25 AM

Kevin Aylward wrote:

gwhite wrote:
Kevin Aylward wrote:

Don Pearce wrote:
On Mon, 01 Sep 2003 14:16:51 +0100, Paul Burridge
wrote:

Is a tuned load (tank circuit) a viable load for an RF amplifier
operating in class A? Or is this type of load only really suitable
for class C?

Of course you can use a tuned load with class A. But the nice thing
about a tuned load is that you don't *have* to use class A to
achieve a clean output. Of course, if you are using an amplitude
modulated signal, then you will need class A.

That's what receivers would use since power consumption doesn't matter
much. It would be true for low level TX'er stages too, again because
of power consumption. But for things like "Ham linears" it is not
necessarily true.

That is, if the input signal is already AM, you need a class A or
linear amplifier.

Let's be specific regarding the your word "linear" since "or" implies
something else other than class-A may be possible.

Yes.

Single-ended
"linear" narrow band amps may be biased class-B if the tank has a high
enough Q. The missing half cycle is restored by the so-called
"flywheel effect." In practice deep AB is also used.

If the AM is to be done at that stage itself, then its the
class c non-linear bit that makes the multiplication modulation work.

No.

No. Its Yes. Non-linear action generates the multiplication products. I
was not drawing any real distinction between class c and b in this
context. The practical difference is minimal. They both do not amplifier
the waveform in a linear manner. I was not meaning to infer that it was
an "only" c. I was referring to the fact that you need at least some
method that generates non linarity.

It can be done with class-A or class-B since the assumption is
that the amp will be driven (or nearly so) to the rails by the carrier
alone.

I agree, this is another method of generating x-product multiplication
terms. However, arguable, a class A amplifier is not really a class A
amplifier if it is driven to saturation. Its a really a switching amp
or, a pulse amplitude modulator if its rails are varying.

Here's a "class-A" amplifier that can be amplitude modulated but yet not
saturated (assumes a constant load R):

V+
|
LC Tank
| AM RF_out
+--||--O
Carrier |
RF_in c
O--||---b Class A biased (no base bias details)
e
|
|
RF_Choke
Audio |
in c
O--||-- b Class A modulator (no base bias details)
e
|
GND

This is a single ended amplitude modulator. The top transistor could be
driven to the switch mode by the carrier, but this is not necessary to
produce AM. Practically, it will be driven to the switch mode for
efficiency reasons.

Amplitude modulation can be "made" via linear methods. "Multipliers"
cannot be generally stated to be either linear or non-linear. A system
which includes a multiplier must be put through the linearity test to
see if the configuration is linear or non-linear. IOW, it can be
either.

+------+
x(t) O---| h(t) |---O y(t)
+------+

linearity:

a·x1(t) = a·y1(t)
b·x2(t) = b·y2(t)

if x(t) = a·x1(t) + b·x2(t)

then

y(t) = a·y1(t) + b·y2(t)

If that is true, then the system is linear. This can be true for
systems with multipliers.

This system is linear and has a multiplier (it is not time invariant):

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| cos(w_c·t) |
+---------------+

It produces a DSB signal (y(t)). w_c·t could be "added in later"
(linearly) to y(t) in the proper amplitude and phase and the resultant
signal would for all practical purposes be indistiguishable from
standard AM. No non-linear circuit was used but yet AM was produced.
Not convenient, but it does dispel the "non-linearity is required"
myth. Also, a multiplier can be viewed as a MISO system.

gwhite

September 5th 03 01:25 AM

Kevin Aylward

September 5th 03 07:43 AM

gwhite wrote:
Kevin Aylward wrote:

gwhite wrote:
Kevin Aylward wrote:

It can be done with class-A or class-B since the assumption is
that the amp will be driven (or nearly so) to the rails by the
carrier alone.

I agree, this is another method of generating x-product
multiplication terms. However, arguable, a class A amplifier is not
really a class A amplifier if it is driven to saturation. Its a
really a switching amp or, a pulse amplitude modulator if its rails
are varying.

Here's a "class-A" amplifier that can be amplitude modulated but yet
not saturated (assumes a constant load R):

Ho hummm...

V+
|
LC Tank
| AM RF_out
+--||--O
Carrier |
RF_in c
O--||---b Class A biased (no base bias details)
e
|
|
RF_Choke
Audio |
in c
O--||-- b Class A modulator (no base bias details)
e
|
GND

This is a single ended amplitude modulator. The top transistor could
be driven to the switch mode by the carrier, but this is not
necessary to produce AM. Practically, it will be driven to the
switch mode for efficiency reasons.

And you think that this is me to me? I suppose you aint read many of my
10,000+ posts.

Err..you've missed the cap from the top transistor emitter to ground. If
the bottom transistor circuit was a true current source at rf, the top
transistor could not effect the output current at all.

Oh, and its not very linear with required to audio input signal without
an emitter resister anyway. The distortion of an basic tranister amp for
2nd Harmonic = Vi(mv)%, that is 10 mv will get you 10% distortion.

Amplitude modulation can be "made" via linear methods.

Nope. Not a chance.

"Multipliers"
cannot be generally stated to be either linear or non-linear.

If one input of a multiplier is held constant, the other input has a
linear response. If the other input is a function of time, the response
to the first input is non-linear. That is, it dose *not* satisfy a(f(t))
= f(at).

The above circuit relies on the fact that the "re" of the top
transistor, is a function of its emitter current set by the bottom
transistor, via the equation re=1/40.Ic. e.g. see
http://www.anasoft.co.uk/EE/index.html

A system which includes a multiplier must be put through the linearity
test to see if the configuration is linear or non-linear. IOW, it
can be either.

Ho humm again. You confuse where the term linearity is to be applied.

+------+
x(t) O---| h(t) |---O y(t)
+------+

linearity:

a·x1(t) = a·y1(t)
b·x2(t) = b·y2(t)

if x(t) = a·x1(t) + b·x2(t)

then

y(t) = a·y1(t) + b·y2(t)

Linearity can more easily be expressed as:

a(f(t)) = f(at)

If that is true, then the system is linear. This can be true for
systems with multipliers.

Nope. A signal being acted on by a multiplier is a non-linear system if
the second input is non constant with time. Your way of base on this
one.

This system is linear and has a multiplier (it is not time invariant):

Nope, its not.

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| cos(w_c·t) |
+---------------+

It produces a DSB signal (y(t)). w_c·t could be "added in later"
(linearly) to y(t) in the proper amplitude and phase and the resultant
signal would for all practical purposes be indistiguishable from
standard AM.

This is not a linear circuit. You need to understand what linear means.
A linear system, cannot produce frequencies that are not in the input,
essentially, by definition. With all due respect, I would guess you
don't have an EE B.S. degree. This is all pretty basic stuff really.

No non-linear circuit was used but yet AM was produced.

Nonsense. Your pretty misguided on this. You can not achieve
multiplication without a non-linear circuit. For example, Gilbert
multipliers use the fact that Id=Is.exp(vd/Vt). That is it logs, adds
and antilog. Balanced switching mixers use switches. Fet mixers use
their square law response.

Not convenient, but it does dispel the "non-linearity is required"
myth.

Its not a myth. I know of no way whatsoever to generate an analogue
multiplication x product terms without having a device satisfying the
property of a.f(t) != f(at), i.e. a non-linear device. Please feel free
to suggest one, but file your patent first.

Oh, by the way...your trying to teach your granny to such eggs son.

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

September 5th 03 07:43 AM

Kevin Aylward

September 5th 03 07:59 AM

Kevin Aylward wrote:

Oh, by the way...your trying to teach your granny to such eggs son.

Should have been:

Oh, by the way...your trying to teach your granny to suck eggs son.

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

September 5th 03 07:59 AM

Roy Lewallen

September 5th 03 08:55 AM

If you're really interested in getting it right, it should have been:

Oh, by the way...you're trying to teach your granny to suck eggs son.

"You're" is a contraction for "you are".
"Your" is an adjective, meaning "of or relating to you or yourself".

And a comma would have been appropriate between "eggs" and "son", making
it better yet if it had read:

Oh, by the way...you're trying to teach your granny to suck eggs, son.

Roy Lewallen, W7EL

Kevin Aylward wrote:
Kevin Aylward wrote:

Oh, by the way...your trying to teach your granny to such eggs son.

Should have been:

Oh, by the way...your trying to teach your granny to suck eggs son.

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.

Roy Lewallen

September 5th 03 08:55 AM

Kevin Aylward

September 5th 03 02:07 PM

Roy Lewallen wrote:
If you're really interested in getting it right, it should have been:

Oh, by the way...you're trying to teach your granny to suck eggs
son.

"You're" is a contraction for "you are".
"Your" is an adjective, meaning "of or relating to you or yourself".

And a comma would have been appropriate between "eggs" and "son",
making it better yet if it had read:

Oh, by the way...you're trying to teach your granny to suck eggs,
son.

Roy Lewallen, W7EL

I stand corrected, but maybe "sonny boy" may have made the point
stronger?

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

September 5th 03 02:07 PM

gwhite

September 6th 03 05:01 AM

Kevin Aylward wrote:

gwhite wrote:
Kevin Aylward wrote:

gwhite wrote:
Kevin Aylward wrote:

It can be done with class-A or class-B since the assumption is
that the amp will be driven (or nearly so) to the rails by the
carrier alone.

I agree, this is another method of generating x-product
multiplication terms. However, arguable, a class A amplifier is not
really a class A amplifier if it is driven to saturation. Its a
really a switching amp or, a pulse amplitude modulator if its rails
are varying.

Here's a "class-A" amplifier that can be amplitude modulated but yet
not saturated (assumes a constant load R):

Ho hummm...

V+
|
LC Tank
| AM RF_out
+--||--O
Carrier |
RF_in c
O--||---b Class A biased (no base bias details)
e
|
|
RF_Choke
Audio |
in c
O--||-- b Class A modulator (no base bias details)
e
|
GND

This is a single ended amplitude modulator. The top transistor could
be driven to the switch mode by the carrier, but this is not
necessary to produce AM. Practically, it will be driven to the
switch mode for efficiency reasons.

And you think that this is me to me? I suppose you aint read many of my
10,000+ posts.

I'm pretty sure I won't bother at this point.

Err..you've missed the cap from the top transistor emitter to ground. If
the bottom transistor circuit was a true current source at rf, the top
transistor could not effect the output current at all.

True. It should be there.

Oh, and its not very linear with required to audio input signal without
an emitter resister anyway. The distortion of an basic tranister amp for
2nd Harmonic = Vi(mv)%, that is 10 mv will get you 10% distortion.

The point wasn't to design a perfect amp. The point was to illustrate
you're wrong.

Amplitude modulation can be "made" via linear methods.

Nope. Not a chance.

Oh, but it can.

"Multipliers"
cannot be generally stated to be either linear or non-linear.

If one input of a multiplier is held constant, the other input has a
linear response. If the other input is a function of time, the response
to the first input is non-linear. That is, it dose *not* satisfy a(f(t))
= f(at).

No, false, or whatever negation pleases you best. You were already
given the answer. You confuse time-invariance with linearity. You need
not take my word for it. Consult any Signals and Sytems text, any
Linear Systems text, or any Communications text. IIRC, the following
was a homework problem in Stremler's text:

Determine linearity
Determine time-invariance

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| cos(w_c·t) |
+---------------+

http://www.amazon.com/exec/obidos/tg...glance&s=books

I suppose if you want to make up your own definition of linearity, you
can get whatever anwswer you wish.

A system which includes a multiplier must be put through the linearity
test to see if the configuration is linear or non-linear. IOW, it
can be either.

Ho humm again. You confuse where the term linearity is to be applied.

I defined the system quite clearly. I mean, I don't think it can be
made simpler.

You can stick with the formal definition given in pretty much every
Signals and Sytems text, any Linear Systems text, or any Communications
text, or you can make up your own and get the answer that pleases you.

+------+
x(t) O---| h(t) |---O y(t)
+------+

linearity:

a·x1(t) = a·y1(t)
b·x2(t) = b·y2(t)

if x(t) = a·x1(t) + b·x2(t)

then

y(t) = a·y1(t) + b·y2(t)

Linearity can more easily be expressed as:

a(f(t)) = f(at)

Except that isn't "the" definition (hey, but it is true if a = 1). It
doesn't even meet you own description:
"A linear system, cannot produce frequencies that are not in the input,
essentially, by definition." -- Kevin Aylward

I would like to see you apply this "definition."

If that is true, then the system is linear. This can be true for
systems with multipliers.

Nope. A signal being acted on by a multiplier is a non-linear system if
the second input is non constant with time. Your way of base on this
one.

Again, you confuse linearity and time-invariance.

This system is linear and has a multiplier (it is not time invariant):

Nope, its not.

Oh, but it is. Some rather trivial math can lead you to understand what
linear means.

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| cos(w_c·t) |
+---------------+

It produces a DSB signal (y(t)). w_c·t could be "added in later"
(linearly) to y(t) in the proper amplitude and phase and the resultant
signal would for all practical purposes be indistiguishable from
standard AM.

This is not a linear circuit. You need to understand what linear means.
A linear system, cannot produce frequencies that are not in the input,
essentially, by definition.

You don't know what linear means. There it is.

With all due respect, I would guess you
don't have an EE B.S. degree.

Cut the chest puffing.

This is all pretty basic stuff really.

On that much we certainly agree, Comm101 ought to do it.

No non-linear circuit was used but yet AM was produced.

Nonsense. Your pretty misguided on this.

Well I won't take you word for it, and you need not take mine. You
could make it easy just by applying the linearity test. That is,
linearity as it is defined in every Signals and Sytems text, any Linear
Systems text, or any Communications text. I'm not as "original" as you,
I simply trust the guys who wrote the books.

You can not achieve
multiplication without a non-linear circuit.

How about this one:

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| 2 |
+---------------+

It looks functionally to be an amp with a gain of two. Is a "gain of 2"
circuit non-linear? Isn't that a multiplier in there?

For example, Gilbert
multipliers use the fact that Id=Is.exp(vd/Vt).

I think that descibes pretty much every bipolar. So I guess transistor
amps cannot be made linear, or at least function sufficiently linear for
the purpose of electronic designers. That is an "interesting"
contention.

That is it logs, adds
and antilog. Balanced switching mixers use switches. Fet mixers use
their square law response.

Not convenient, but it does dispel the "non-linearity is required"
myth.

Its not a myth. I know of no way whatsoever to generate an analogue
multiplication x product terms without having a device satisfying the
property of a.f(t) != f(at), i.e. a non-linear device. Please feel free
to suggest one, but file your patent first.

Why not dispense with the snidery, and simply prove your contention by
applying the linearity test to this one:

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| cos(w_c·t) |
+---------------+

Hey, I'll even give you a hint.

Let x1(t) = a1·cos(w1·t)
x2(t) = a2·cos(w2·t)

Then y1(t) = a1·cos([wc + w1]·t)/2 + a1·cos([wc - w1]·t)/2
y2(t) = a2·cos([wc + w1]·t)/2 + a2·cos([wc - w1]·t)/2

?
If x(t) = x1(t) + x2(t) does y(t) = y1(t) + y2(t)
(This *is* the linearity test.)

?
[x1(t) + x2(t)]·cos(wc·t) = x1(t)·cos(wc·t) + x2(t)·cos(wc·t) = y(t)

The answer is yes: the system is linear, by the linearity test.

If x(t) = a·cos(w·t) is applied to the system,
and produces y(t), does x(t-to) applied to the
system result in y(t) except all the t's are
replaced by t-to? (May all the t's in
the y(t) case be replaced by t-to, and
have the system response reflect that the input
was x(t-to).) (This is the time-invariance test.)

y(t) = x(t)·cos(wc·t) = a·cos(w·t)·cos(wc·t)
= a·cos([wc + w]·t)/2 + a·cos([wc - w]·t)/2

Now put the "to" into the input and see what
comes out

What? = x(t-to)·cos(wc·t) = a·cos(w·[t-to])·cos(wc·t)
= a·cos([wc·t + w·[t-to])/2 + a·cos([wc·t - w·[t-to])/2
| |
+---------------------------+
not t-to,

So the system is *not* time-invariant.

This is Comm101 stuff, if you're ever interested enough to crack a book
open, and actually work the problems.

Oh, by the way...your trying to teach your granny to such eggs son.

You're wrong about that one too: we have no relationship. I hope that
comforts you, as I know it does me.

gwhite

September 6th 03 05:01 AM

Kevin Aylward

September 6th 03 10:25 AM

gwhite wrote:
Kevin Aylward wrote:

"Multipliers"
cannot be generally stated to be either linear or non-linear.

If one input of a multiplier is held constant, the other input has a
linear response. If the other input is a function of time, the
response to the first input is non-linear. That is, it dose *not*
satisfy a(f(t)) = f(at).

No, false, or whatever negation pleases you best.

No its correct. If the second input is time varying the output of the
system is *not* a linear function of the first input. Its that simple.

You were already
given the answer. You confuse time-invariance with linearity.

Not at all.

You
need not take my word for it.

I dont.

Consult any Signals and Sytems text,
any Linear Systems text, or any Communications text. IIRC, the
following was a homework problem in Stremler's text:

So, the book is out to lunch, or your interpretation of it is. So what.

Determine linearity
Determine time-invariance

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| cos(w_c·t) |
+---------------+

http://www.amazon.com/exec/obidos/tg...glance&s=books

I suppose if you want to make up your own definition of linearity, you
can get whatever anwswer you wish.

Indeed.

Linearity can more easily be expressed as:

a(f(t)) = f(at)

Except that isn't "the" definition (hey, but it is true if a = 1). It
doesn't even meet you own description:

I did not say it was. I was keeping it simple.

"A linear system, cannot produce frequencies that are not in the
input, essentially, by definition." -- Kevin Aylward

I would like to see you apply this "definition."

I do. It makes a reasonably good practical definition.

If that is true, then the system is linear. This can be true for
systems with multipliers.

Nope. A signal being acted on by a multiplier is a non-linear system
if the second input is non constant with time. Your way of base on
this one.

Again, you confuse linearity and time-invariance.

Nope. I agree, if, for example, a second input is constant in time, a
circuit can be linear, however, if a second input changes the gain of
the first signal then the output is no longer a simple gain + offset,
therefore, the system in non-linear. The output is not a "simple"
function of the input.

However, I agree, "I suppose if you want to make up your own definition
of linearity you can get whatever answer you wish."

This system is linear and has a multiplier (it is not time
invariant):

Nope, its not.

Oh, but it is.

It is not...

Some rather trivial math can lead you to understand
what linear means.

Ho hum sniped.

No non-linear circuit was used but yet AM was produced.

Nonsense. Your pretty misguided on this.

Well I won't take you word for it, and you need not take mine.

I don't. Its 101 transistor electronics that the collector current
follows the base voltage by an exponential relation. The class A amp you
showed achieved multiplication because:

gm=40.Ic. because gm=di/dv, directly obtained from I=io.exp(Vb/Vt)

So that Vo=40.Ic.Vc

therefore

Vo = 40.Vc.Vi/Re

So, the modulation is achieved precisely because the transistor is
non-linear. This clearly contradicts your claim that your stated class A
amp is a modulator without using non linear properties.

Please present your detailed, alternative argument to support your claim
that your class A amp does not rely on non linearity to achieve
modulation, and why my 101 analysis, as given above, is false.

You
could make it easy just by applying the linearity test. That is,
linearity as it is defined in every Signals and Sytems text, any
Linear Systems text, or any Communications text. I'm not as
"original" as you, I simply trust the guys who wrote the books.

I don't. Furthermore, I don't trust your claim.

You can not achieve
multiplication without a non-linear circuit.

How about this one:

The System
+---------------+
| |
in | /¯¯¯\ | out
x(t) O--------( X )---------O y(t)
| \___/ |
| | |
| | |
| O |
| 2 |
+---------------+

It looks functionally to be an amp with a gain of two. Is a "gain of
2" circuit non-linear? Isn't that a multiplier in there?

Your grasping at straws here. This is trivially not the point. Of course
a fixed, or constant gain on a signal is linear. Jesus wept dude. No
brownie points for you on this one, I'm afraid. It was clear from the
start that one is referring to varying multiplication.

For example, Gilbert
multipliers use the fact that Id=Is.exp(vd/Vt).

I think that descibes pretty much every bipolar. So I guess
transistor amps cannot be made linear, or at least function
sufficiently linear for the purpose of electronic designers. That is
an "interesting" contention.

Out to lunch again. Of course transistors amps can be made as linear as
desired, I made no such connotation. Again, your making up what I say as
you go along because you arguments are so weak.

My point on the class A, non clipping, amp modulator you showed above,
it that it *relies* *explicitly* on the non-linear transfer function to
achieve multiplication.

Again, present your theoretical argument as to how AM modulation
actually occurs in said amplifier, without using any properties derived
from any non-linear behaviour.

That is it logs, adds
and antilog. Balanced switching mixers use switches. Fet mixers use
their square law response.

Not convenient, but it does dispel the "non-linearity is required"
myth.

Its not a myth. I know of no way whatsoever to generate an analogue
multiplication x product terms without having a device satisfying the
property of a.f(t) != f(at), i.e. a non-linear device. Please feel
free to suggest one, but file your patent first.

Why not dispense with the snidery, and simply prove your contention by
applying the linearity test to this one:

I must confess here I made a small error. Contrary to my claim of
ignorance, I am in fact aware of a modulating technique that dose not
rely, it would appear, on a devices non linearity, and have been so
aware for a considerable time, but it slipped my mind. A light dependant
resistor and a light bulb would seem to satisfy this requirement. I
suspect the claim would have to be modified to a direct electrical
method. I await you providing an example.

{pretentious drivel sniped}

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

September 6th 03 10:25 AM

Kevin Aylward

September 6th 03 11:44 AM

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. A point was made that a class A
transistor amp modulator achieves modulation via completely linear
means. This is clearly not correct as was showed in my last post, and in
engineering practise, its probably impossible to generate a modulation
function, in a direct electrical circuit, without explicitly using an
inherent nonlinearity of a device. One only has to look at any practical
modulator. That is, modulation and non-linearity, is isomorphic in a
practical sense. However, there is certainly a valid argument, that in a
strict mathematical technical sense, a "linear" system can encompass a
much wider class of systems all under the banner of "linear". This is
pretty much obvious, for example, even a Bessel integral transform is a
"linear" transform, but would actually severely distort a signal
considerable. However, this extended view of "linear" has little do with
real analogue circuits, where linear is generally accepted to mean
linear gain with offset, and is a technicality that has little, or even
no value at all. The point has been made, but there is yet to be any
real physical example presented, where such a technical point has any
practical merit in real circuits.

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

September 6th 03 11:44 AM

Paul Burridge

September 6th 03 02:45 PM

With all due respect, I would guess you
don't have an EE B.S. degree.

Cut the chest puffing.

Chest-puffing is one of Kev's more prominent character traits, I'm
afraid. In fact one often gets the impression that his contributions
to these threads is more contrived to show off his knowledge of
electonics and mathematics than to help others out of pure, selfless
altruism.
Anyway, personal insults aside, I for one am lurking with interest to
see who prevails in this linearity argument. It's a pity some
heavyweight like Win can't step in and judge who's in the right on
this one but I rather suspect he has better things to do with his
time. Sadly I haven't so will continue to read these posts with
interest!
--

"I believe history will be kind to me, since I intend
to write it." - Winston Churchill

Paul Burridge

September 6th 03 02:45 PM

Kevin Aylward

September 6th 03 04:29 PM

Paul Burridge wrote:
With all due respect, I would guess you
don't have an EE B.S. degree.

Cut the chest puffing.

Chest-puffing is one of Kev's more prominent character traits, I'm
afraid. In fact one often gets the impression that his contributions
to these threads is more contrived to show off his knowledge of
electonics and mathematics

Not at all. The purpose of my contributions are as a means of getting
attention to my product, thereby gaining me much Guinness.

than to help others out of pure, selfless
altruism.

Where on earth did you get this daft idea that I post for the good of
the people? As I have noted many times, there is no such thing as
selfless altruism, its all for ulterior motives. We are all inherently
selfish. I absolute agree that everything I do is ultimately geared
toward my self interest, or to be more exact, the self interest of my
genes. I have never claimed otherwise. Anyone who claims that they take
action for the benefit of others, at a net determinate to themselves are
either, liars, fools, or deluded.

Anyway, personal insults aside, I for one am lurking with interest to
see who prevails in this linearity argument. It's a pity some
heavyweight like Win can't step in and judge who's in the right on

With all due respect to you here, why do you suppose that Win, and with
all due respect to Winfred, is more qualified than myself on electronics
matters.?

this one but I rather suspect he has better things to do with his
time.

This one is easy. I'm right. As far as the class A amp goes, its a no
contest. It can't possible form a modulator without relying on the
non-linear behaviour of the transistor. Its not debatable. I have
explained the details already.

Regarding the definition of linearity, it is an open book. There is no
single absolute correct definition. What we have here is a play on
words, where some one is claiming that his version of the word
definition is the only valid one, even whem most don't use it that way.
A linear operator in mathematics, or linearity, is used in a different
sense then it is used in analogue design. An object that satisfies the
definition of a linear system in mathematics, is not one that is usually
applicable to analogue design, and as used by, essentially, all analogue
designers. The analogue definition of linearity is much more
restrictive. For example, a linear amplifier in electronics is generally
restricted to those amplifiers such that the output voltage or current
is a simple constant times the input voltage or current, with or without
an offset. That is, there is a *linear* = *straight* *line* relation
between output and input. This is equivalent to requiring that the
output only contains frequencies present at its input, i.e. no
distortion. Some other mathematical definitions of linearity would not
be so restrictive. For example, suppose a signal is fed through a magic
analogue Fourier transform device that converts the input voltage to
that of its Fourier transform. You would be hard pressed to get someone
to agree that the output signal is not a gross distortion of its input,
despite the fact that the Fourier transform is mathematically a linear
transform. Sure, some high brow might like to claim that his definition
is the "real" one, but words only mean what the majority means by them,
and in this case, a "linear" system, is one with a straight/linear line
relation between input and output.

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

September 6th 03 04:29 PM

Paul Burridge

September 6th 03 06:19 PM

On Sat, 6 Sep 2003 16:29:49 +0100, "Kevin Aylward"
wrote:

Not at all. The purpose of my contributions are as a means of getting
attention to my product, thereby gaining me much Guinness.

Oh yes. There's the product-plugging as well. I'd forgotten about
that.

Where on earth did you get this daft idea that I post for the good of
the people? As I have noted many times, there is no such thing as
selfless altruism, its all for ulterior motives. We are all inherently
selfish. I absolute agree that everything I do is ultimately geared
toward my self interest, or to be more exact, the self interest of my
genes. I have never claimed otherwise. Anyone who claims that they take
action for the benefit of others, at a net determinate to themselves are
either, liars, fools, or deluded.

I disagree. You personally may well be motivated by selfishness as I
don't doubt are very many people. But to say that everyone's like you
is nonsense, quite frankly. There have been ample demonstrations of
others' ability to be helpful for no self-gain whatsoever on this
newsgroup alone. But I give you credit for making no bones about your
motivations anyway. :-)

With all due respect to you here, why do you suppose that Win, and with
all due respect to Winfred, is more qualified than myself on electronics
matters.?

Er, the guy's a senior professor of electonics at Harvard, Kev. He
probably knows more about the subject than the rest of us put
together.

This one is easy. I'm right. As far as the class A amp goes, its a no
contest. It can't possible form a modulator without relying on the
non-linear behaviour of the transistor. Its not debatable. I have
explained the details already.

Well clearly it *is* debatable from what I've seen in this thread! You
simply believe you know best and that's that.

Regarding the definition of linearity, it is an open book. There is no
single absolute correct definition. What we have here is a play on
words, where some one is claiming that his version of the word
definition is the only valid one, even whem most don't use it that way.
A linear operator in mathematics, or linearity, is used in a different
sense then it is used in analogue design. An object that satisfies the
definition of a linear system in mathematics, is not one that is usually
applicable to analogue design, and as used by, essentially, all analogue
designers. The analogue definition of linearity is much more
restrictive. For example, a linear amplifier in electronics is generally
restricted to those amplifiers such that the output voltage or current
is a simple constant times the input voltage or current, with or without
an offset. That is, there is a *linear* = *straight* *line* relation
between output and input. This is equivalent to requiring that the
output only contains frequencies present at its input, i.e. no
distortion. Some other mathematical definitions of linearity would not
be so restrictive. For example, suppose a signal is fed through a magic
analogue Fourier transform device that converts the input voltage to
that of its Fourier transform. You would be hard pressed to get someone
to agree that the output signal is not a gross distortion of its input,
despite the fact that the Fourier transform is mathematically a linear
transform. Sure, some high brow might like to claim that his definition
is the "real" one, but words only mean what the majority means by them,
and in this case, a "linear" system, is one with a straight/linear line
relation between input and output.

I can't argue with any of that, but there again I'm no expert. I have
to say, though, that I've always found it very curious that radio hams
refer to their bolt-on, high-power, aftermarket boosters as "linear
amplifiers." You can't get any *less* linear than class C!
Or can you?
--

"I believe history will be kind to me, since I intend
to write it." - Winston Churchill

Paul Burridge

September 6th 03 06:19 PM

Kevin Aylward

September 6th 03 07:18 PM

Paul Burridge wrote:
On Sat, 6 Sep 2003 16:29:49 +0100, "Kevin Aylward"
wrote:

Not at all. The purpose of my contributions are as a means of getting
attention to my product, thereby gaining me much Guinness.

Oh yes. There's the product-plugging as well. I'd forgotten about
that.

Where on earth did you get this daft idea that I post for the good of
the people? As I have noted many times, there is no such thing as
selfless altruism, its all for ulterior motives. We are all
inherently selfish. I absolute agree that everything I do is
ultimately geared toward my self interest, or to be more exact, the
self interest of my genes. I have never claimed otherwise. Anyone
who claims that they take action for the benefit of others, at a net
determinate to themselves are either, liars, fools, or deluded.

I disagree. You personally may well be motivated by selfishness as I
don't doubt are very many people.

Er.. we all are. Its explained in "The selfish gene" by Richard Dawkins.
Its a basic tenet of the modern theory of evolution.

But to say that everyone's like you
is nonsense, quite frankly.

Not at all. You must be one of the deluded ones. That is, you haven't
really thought about or studied evolution in enough detail. I am sure
you are genuine in this belief, but you are wrong. Of course, if you are
a believer in god or some other religion, then nothing I can say will
convince you otherwise.

There have been ample demonstrations of
others' ability to be helpful for no self-gain whatsoever on this
newsgroup alone.

You miss the point. The term is *net* benefit or advantage. You need to
look at this *much* more deeply. Its only an illusion that one does
things for the benefit of others.

I have explained this quite a few times. Its based on the theory of
replicators.

Axioms:

1 Traits are passed on to offspring.
2 Traits are randamlly generated.
3 Traits are selected by the environment.

Now consider replicater A, that replicates *consistently* better than
replicater B, say by 1%, due to a certain trait. After 1000
generations, what is the distribution of A/B?

This all takes time to explain in detail, but the gist is if any
replicater takes an action that results in a *net* *final* disadvantage,
the other replicators, will replicate themselves better. Its simple
math. We can only observe the best replicators.

Obviously, it gets quite complicated, if doing some good to another, can
result in a net beifit by returned favours, then a replicater will do
so. Nevertheless its still inherently "selfish". In addition, a trait
might not be consistently better, e.g. the larger one gets that enables
one to fend for themselves better, is mitigated by the fact that one
needs more food and other resources.

Have a look on the web for "the selfish gene" or get the book.

But I give you credit for making no bones about your
motivations anyway. :-)

I was not suggesting that I am always consciously doing things in a
selfish manner. I am accepting the fact that its inherent from millions
of years of evolution that we are all basically selfish, and there not
much we can do about it.

With all due respect to you here, why do you suppose that Win, and
with all due respect to Winfred, is more qualified than myself on
electronics matters.?

Er, the guy's a senior professor of electonics at Harvard, Kev. He
probably knows more about the subject than the rest of us put
together.

Whilst, I do agree that Win is very knowledgeable and an expert, I am
also an expert. I have been doing this rather a long time as well you
know. The fact that I am not an academic is not relevant. In all
honesty, there is not much I don't know about general analogue design,
although, obviously, I don't claim to know it all. Does Win know more
than me? Unlikely. Or do I know more than Win. Unlikely. However, we may
well know different things.

This one is easy. I'm right. As far as the class A amp goes, its a no
contest. It can't possible form a modulator without relying on the
non-linear behaviour of the transistor. Its not debatable. I have
explained the details already.

Well clearly it *is* debatable from what I've seen in this thread! You
simply believe you know best and that's that.

But this part of it isnt. I gave the analysis of how the class A
modulator actually works. Its a fact. Its a standard and accepted result
by anyone knowledgably in the field.

I don't claim that gwhite's definition of linearity is inherently wrong,
only that it is not the one used in general analogue design. My argument
was not about the definition of linearity, it was about gwhite's claim
that his class A amp achieved a modulation function *without* relying on
the inherent non linearity of the transistors emitter current verses
vbe. This claim is absolutely false.

Regarding the definition of linearity, it is an open book. There is
no single absolute correct definition. What we have here is a play on
words, where some one is claiming that his version of the word
definition is the only valid one, even whem most don't use it that
way. A linear operator in mathematics, or linearity, is used in a
different sense then it is used in analogue design. An object that
satisfies the definition of a linear system in mathematics, is not
one that is usually applicable to analogue design, and as used by,
essentially, all analogue designers. The analogue definition of
linearity is much more restrictive. For example, a linear amplifier
in electronics is generally restricted to those amplifiers such that
the output voltage or current is a simple constant times the input
voltage or current, with or without an offset. That is, there is a
*linear* = *straight* *line* relation between output and input. This
is equivalent to requiring that the output only contains frequencies
present at its input, i.e. no distortion. Some other mathematical
definitions of linearity would not be so restrictive. For example,
suppose a signal is fed through a magic analogue Fourier transform
device that converts the input voltage to that of its Fourier
transform. You would be hard pressed to get someone to agree that
the output signal is not a gross distortion of its input, despite
the fact that the Fourier transform is mathematically a linear
transform. Sure, some high brow might like to claim that his
definition is the "real" one, but words only mean what the majority
means by them, and in this case, a "linear" system, is one with a
straight/linear line relation between input and output.

I can't argue with any of that, but there again I'm no expert. I have
to say, though, that I've always found it very curious that radio hams
refer to their bolt-on, high-power, aftermarket boosters as "linear
amplifiers." You can't get any *less* linear than class C!
Or can you?

And that illustrates the point very well. Linearity is up for grabs.
Just what is the term "linear" being applied to. Average power,
instantaneous voltage...

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

September 6th 03 07:18 PM

Michael Black

September 7th 03 02:56 AM

"Dick Carroll;" ) writes:
Paul Burridge wrote:

I have
to say, though, that I've always found it very curious that radio hams
refer to their bolt-on, high-power, aftermarket boosters as "linear
amplifiers." You can't get any *less* linear than class C!

??? ....I won't speak for the rest of ham radio, but I've never operated a linear
amplifier in Class C.

Dick

Well when you've got it on 2meters and are feeding it with an FM rig,
of course it's silly to call it a "linear amplifier".

Michael VE2BVW

Michael Black

September 7th 03 02:56 AM

Kevin Aylward

September 7th 03 08:04 AM

Paul Burridge wrote:
On Sat, 6 Sep 2003 16:29:49 +0100, "Kevin Aylward"
wrote:

Not at all. The purpose of my contributions are as a means of getting
attention to my product, thereby gaining me much Guinness.

Oh yes. There's the product-plugging as well. I'd forgotten about
that.

Where on earth did you get this daft idea that I post for the good of
the people? As I have noted many times, there is no such thing as
selfless altruism, its all for ulterior motives. We are all
inherently selfish. I absolute agree that everything I do is
ultimately geared toward my self interest, or to be more exact, the
self interest of my genes. I have never claimed otherwise. Anyone
who claims that they take action for the benefit of others, at a net
determinate to themselves are either, liars, fools, or deluded.

I disagree. You personally may well be motivated by selfishness as I
don't doubt are very many people.

Er.. we all are. Its explained in "The selfish gene" by Richard Dawkins.
Its a basic tenet of the modern theory of evolution.

But to say that everyone's like you
is nonsense, quite frankly.

Not at all. You must be one of the deluded ones. That is, you haven't
really thought about or studied evolution in enough detail. I am sure
you are genuine in this belief, but you are wrong. Of course, if you are
a believer in god or some other religion, then nothing I can say will
convince you otherwise.

There have been ample demonstrations of
others' ability to be helpful for no self-gain whatsoever on this
newsgroup alone.

You miss the point. The term is *net* benefit or advantage. You need to
look at this *much* more deeply. Its only an illusion that one does
things for the benefit of others.

I have explained this quite a few times. Its based on the theory of
replicators.

Axioms:

1 Traits are passed on to offspring.
2 Traits are randamlly generated.
3 Traits are selected by the environment.

Now consider replicater A, that replicates *consistently* better than
replicater B, say by 1%, due to a certain trait. After 1000
generations, what is the distribution of A/B?

This all takes time to explain in detail, but the gist is if any
replicater takes an action that results in a *net* *final* disadvantage,
the other replicators, will replicate themselves better. Its simple
math. We can only observe the best replicators.

Obviously, it gets quite complicated, if doing some good to another, can
result in a net beifit by returned favours, then a replicater will do
so. Nevertheless its still inherently "selfish". In addition, a trait
might not be consistently better, e.g. the larger one gets that enables
one to fend for themselves better, is mitigated by the fact that one
needs more food and other resources.

Have a look on the web for "the selfish gene" or get the book.

But I give you credit for making no bones about your
motivations anyway. :-)

I was not suggesting that I am always consciously doing things in a
selfish manner. I am accepting the fact that its inherent from millions
of years of evolution that we are all basically selfish, and there not
much we can do about it.

With all due respect to you here, why do you suppose that Win, and
with all due respect to Winfred, is more qualified than myself on
electronics matters.?

Er, the guy's a senior professor of electonics at Harvard, Kev. He
probably knows more about the subject than the rest of us put
together.

Whilst, I do agree that Win is very knowledgeable and an expert, I am
also an expert. I have been doing this rather a long time as well you
know. The fact that I am not an academic is not relevant. In all
honesty, there is not much I don't know about general analogue design,
although, obviously, I don't claim to know it all. Does Win know more
than me? Unlikely. Or do I know more than Win. Unlikely. However, we may
well know different things.

This one is easy. I'm right. As far as the class A amp goes, its a no
contest. It can't possible form a modulator without relying on the
non-linear behaviour of the transistor. Its not debatable. I have
explained the details already.

Well clearly it *is* debatable from what I've seen in this thread! You
simply believe you know best and that's that.

But this part of it isnt. I gave the analysis of how the class A
modulator actually works. Its a fact. Its a standard and accepted result
by anyone knowledgably in the field.

I don't claim that gwhite's definition of linearity is inherently wrong,
only that it is not the one used in general analogue design. My argument
was not about the definition of linearity, it was about gwhite's claim
that his class A amp achieved a modulation function *without* relying on
the inherent non linearity of the transistors emitter current verses
vbe. This claim is absolutely false.

Regarding the definition of linearity, it is an open book. There is
no single absolute correct definition. What we have here is a play on
words, where some one is claiming that his version of the word
definition is the only valid one, even whem most don't use it that
way. A linear operator in mathematics, or linearity, is used in a
different sense then it is used in analogue design. An object that
satisfies the definition of a linear system in mathematics, is not
one that is usually applicable to analogue design, and as used by,
essentially, all analogue designers. The analogue definition of
linearity is much more restrictive. For example, a linear amplifier
in electronics is generally restricted to those amplifiers such that
the output voltage or current is a simple constant times the input
voltage or current, with or without an offset. That is, there is a
*linear* = *straight* *line* relation between output and input. This
is equivalent to requiring that the output only contains frequencies
present at its input, i.e. no distortion. Some other mathematical
definitions of linearity would not be so restrictive. For example,
suppose a signal is fed through a magic analogue Fourier transform
device that converts the input voltage to that of its Fourier
transform. You would be hard pressed to get someone to agree that
the output signal is not a gross distortion of its input, despite
the fact that the Fourier transform is mathematically a linear
transform. Sure, some high brow might like to claim that his
definition is the "real" one, but words only mean what the majority
means by them, and in this case, a "linear" system, is one with a
straight/linear line relation between input and output.

I can't argue with any of that, but there again I'm no expert. I have
to say, though, that I've always found it very curious that radio hams
refer to their bolt-on, high-power, aftermarket boosters as "linear
amplifiers." You can't get any *less* linear than class C!
Or can you?

And that illustrates the point very well. Linearity is up for grabs.
Just what is the term "linear" being applied to. The class c amplifier
is non linear in detailed operation but the envelope of the output is
still linearly related to the modulating input signal.

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

September 7th 03 08:04 AM

Paul Burridge wrote:
On Sat, 6 Sep 2003 16:29:49 +0100, "Kevin Aylward"
wrote:

Not at all. The purpose of my contributions are as a means of getting
attention to my product, thereby gaining me much Guinness.

Oh yes. There's the product-plugging as well. I'd forgotten about
that.

Where on earth did you get this daft idea that I post for the good of
the people? As I have noted many times, there is no such thing as
selfless altruism, its all for ulterior motives. We are all
inherently selfish. I absolute agree that everything I do is
ultimately geared toward my self interest, or to be more exact, the
self interest of my genes. I have never claimed otherwise. Anyone
who claims that they take action for the benefit of others, at a net
determinate to themselves are either, liars, fools, or deluded.

I disagree. You personally may well be motivated by selfishness as I
don't doubt are very many people.

Er.. we all are. Its explained in "The selfish gene" by Richard Dawkins.
Its a basic tenet of the modern theory of evolution.

But to say that everyone's like you
is nonsense, quite frankly.

Not at all. You must be one of the deluded ones. That is, you haven't
really thought about or studied evolution in enough detail. I am sure
you are genuine in this belief, but you are wrong. Of course, if you are
a believer in god or some other religion, then nothing I can say will
convince you otherwise.

There have been ample demonstrations of
others' ability to be helpful for no self-gain whatsoever on this
newsgroup alone.

You miss the point. The term is *net* benefit or advantage. You need to
look at this *much* more deeply. Its only an illusion that one does
things for the benefit of others.

I have explained this quite a few times. Its based on the theory of
replicators.

Axioms:

1 Traits are passed on to offspring.
2 Traits are randamlly generated.
3 Traits are selected by the environment.

Now consider replicater A, that replicates *consistently* better than
replicater B, say by 1%, due to a certain trait. After 1000
generations, what is the distribution of A/B?

This all takes time to explain in detail, but the gist is if any
replicater takes an action that results in a *net* *final* disadvantage,
the other replicators, will replicate themselves better. Its simple
math. We can only observe the best replicators.

Obviously, it gets quite complicated, if doing some good to another, can
result in a net beifit by returned favours, then a replicater will do
so. Nevertheless its still inherently "selfish". In addition, a trait
might not be consistently better, e.g. the larger one gets that enables
one to fend for themselves better, is mitigated by the fact that one
needs more food and other resources.

Have a look on the web for "the selfish gene" or get the book.

But I give you credit for making no bones about your
motivations anyway. :-)

I was not suggesting that I am always consciously doing things in a
selfish manner. I am accepting the fact that its inherent from millions
of years of evolution that we are all basically selfish, and there not
much we can do about it.

With all due respect to you here, why do you suppose that Win, and
with all due respect to Winfred, is more qualified than myself on
electronics matters.?

Er, the guy's a senior professor of electonics at Harvard, Kev. He
probably knows more about the subject than the rest of us put
together.

Whilst, I do agree that Win is very knowledgeable and an expert, I am
also an expert. I have been doing this rather a long time as well you
know. The fact that I am not an academic is not relevant. In all
honesty, there is not much I don't know about general analogue design,
although, obviously, I don't claim to know it all. Does Win know more
than me? Unlikely. Or do I know more than Win. Unlikely. However, we may
well know different things.

This one is easy. I'm right. As far as the class A amp goes, its a no
contest. It can't possible form a modulator without relying on the
non-linear behaviour of the transistor. Its not debatable. I have
explained the details already.

Well clearly it *is* debatable from what I've seen in this thread! You
simply believe you know best and that's that.

But this part of it isnt. I gave the analysis of how the class A
modulator actually works. Its a fact. Its a standard and accepted result
by anyone knowledgably in the field.

I don't claim that gwhite's definition of linearity is inherently wrong,
only that it is not the one used in general analogue design. My argument
was not about the definition of linearity, it was about gwhite's claim
that his class A amp achieved a modulation function *without* relying on
the inherent non linearity of the transistors emitter current verses
vbe. This claim is absolutely false.

Regarding the definition of linearity, it is an open book. There is
no single absolute correct definition. What we have here is a play on
words, where some one is claiming that his version of the word
definition is the only valid one, even whem most don't use it that
way. A linear operator in mathematics, or linearity, is used in a
different sense then it is used in analogue design. An object that
satisfies the definition of a linear system in mathematics, is not
one that is usually applicable to analogue design, and as used by,
essentially, all analogue designers. The analogue definition of
linearity is much more restrictive. For example, a linear amplifier
in electronics is generally restricted to those amplifiers such that
the output voltage or current is a simple constant times the input
voltage or current, with or without an offset. That is, there is a
*linear* = *straight* *line* relation between output and input. This
is equivalent to requiring that the output only contains frequencies
present at its input, i.e. no distortion. Some other mathematical
definitions of linearity would not be so restrictive. For example,
suppose a signal is fed through a magic analogue Fourier transform
device that converts the input voltage to that of its Fourier
transform. You would be hard pressed to get someone to agree that
the output signal is not a gross distortion of its input, despite
the fact that the Fourier transform is mathematically a linear
transform. Sure, some high brow might like to claim that his
definition is the "real" one, but words only mean what the majority
means by them, and in this case, a "linear" system, is one with a
straight/linear line relation between input and output.

I can't argue with any of that, but there again I'm no expert. I have
to say, though, that I've always found it very curious that radio hams
refer to their bolt-on, high-power, aftermarket boosters as "linear
amplifiers." You can't get any *less* linear than class C!
Or can you?

And that illustrates the point very well. Linearity is up for grabs.
Just what is the term "linear" being applied to. The class c amplifier
is non linear in detailed operation but the envelope of the output is
still linearly related to the modulating input signal.

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.

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