On Wed, 10 Sep 2003 10:25:49 +0100, "Kevin Aylward"
wrote:


That is, to achieve linear multiplication by this transistor gm method,
it necessarily requires a non-linear relation between I and V for the
transistors gm characteristics. This forms a proof of my statement that
the class A modulator achieves such modulation by a non-linear process.

gwhite:

Please do not respond if you are going to past masses of waffle text
that you don't understand. Provide a *mathematical* *explicit* disproof
of my mathematics or present your retraction.

Well this is compelling stuff, I must say. I'd hoped to be able to
disappear on holiday for a week and return refreshed, but it looks
like I'm going to have to seek out cybercafes to keep up to date on
these exchanges instead. :-( Still no outright winner so far...


--

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

Paul Burridge wrote:
On Wed, 10 Sep 2003 10:25:49 +0100, "Kevin Aylward"
wrote:


That is, to achieve linear multiplication by this transistor gm
method, it necessarily requires a non-linear relation between I and
V for the transistors gm characteristics. This forms a proof of my
statement that the class A modulator achieves such modulation by a
non-linear process.

gwhite:

Please do not respond if you are going to past masses of waffle text
that you don't understand. Provide a *mathematical* *explicit*
disproof of my mathematics or present your retraction.

Well this is compelling stuff, I must say. I'd hoped to be able to
disappear on holiday for a week and return refreshed, but it looks
like I'm going to have to seek out cybercafes to keep up to date on
these exchanges instead. :-( Still no outright winner so far...

Not to me aint. The case is closed.

The problem with gwhite, is that his arguments are all based on "an
appeal to authority", and we all know that is not the way science is
done. He pastes reams of stuff without the slightest idea of what the
documents are talking about. The assumption being that such documents
back him up. They don't. He hasn't presented one, not even one
derivation of his claim, only end results. This is typical of all
vacuous claims. It says so in the bible, so it must be true sort of
thing.

On the otherhand, he does have a very valid point that one, could in
principle, make a modulator that does not depend on an inherent
non-linearity, he just happened to pick the wrong examples, and the
wrong person to debate with. He obviously learnt the basic concept from
a coarse he took, but never understood
enough to know when and how to apply it. For the active bipolar or fet
case, the gain setting is gm based, and this gm is electrically
controlled by the value of its
own current, hence, as a I proved, must have a non-linear V/I curve.
However, for example, in a passive case, things are different. If one
used a fet as a passive voltage controlled resister, the resistance is a
function of the gate source voltage, but the control voltage is not
connected accross the controlled resistance, and the resistance
variation is not implied to be a function of its own current, therefore
a non-linear resistance is not implied. Indeed, this technique is used
in guitar phaser pedals to produce a swept notch filter, and I designed
and built my
first one of those around 25 years ago, based on this concept. To make
the fet even more linear, as qwhite correctly suggested, I used, as is
well known standard practice, a series gate resister and feedback
resistor from drain to gate. Unfortunately, I made a mistake...in my
"there is only a world market for 5 computers" statement, I forgot what
I already knew:-)

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:



Provide a *mathematical* *explicit*
disproof of my mathematics or present your retraction.

You are correct about the specific device (BJTs) biased class-A for
multipliers such as the gilbert cell. They need to have the gm "slope"
change for the gain to change, and changing the gain is what the
modulation is all about. By definition that means those "slopes" are
tangent to something that can't be straight (the Vbe - Ic function).
I was wrong about the specific device used in this type of application.
The system in this application (DSB-AM) is most certainly linear (all
phase and amplitude information is completely preserved -- the definition
of linearity -- albeit at a translated frequency), but the Vbe - Ic
function for the transistor isn't linear and it can't be for it to work
in the given configuration.






· Gain is a direct function of gm.
· Gain must change for amplitude modulation to occur, by definition.
..·. not only must gm move along the curve, the curve has to be a
curve (not straight), otherwise the gain would not change.


Ic Ic = f(Vbe)
| .
| . .slope of Vbe - Ic = gm
| . .
| . .
| . .
| . .
Ic_q+--------------..
| .. |
| . . |
| . . |
| . . |
|. . |
| . |
+---------------+------------- Vbe
Vbeq

Pretty simple really. No wonder I was so bored and fell asleep in EDSN101.

Kevin Aylward wrote:



Provide a *mathematical* *explicit*
disproof of my mathematics or present your retraction.

You are correct about the specific device (BJTs) biased class-A for
multipliers such as the gilbert cell. They need to have the gm "slope"
change for the gain to change, and changing the gain is what the
modulation is all about. By definition that means those "slopes" are
tangent to something that can't be straight (the Vbe - Ic function).
I was wrong about the specific device used in this type of application.
The system in this application (DSB-AM) is most certainly linear (all
phase and amplitude information is completely preserved -- the definition
of linearity -- albeit at a translated frequency), but the Vbe - Ic
function for the transistor isn't linear and it can't be for it to work
in the given configuration.






· Gain is a direct function of gm.
· Gain must change for amplitude modulation to occur, by definition.
..·. not only must gm move along the curve, the curve has to be a
curve (not straight), otherwise the gain would not change.


Ic Ic = f(Vbe)
| .
| . .slope of Vbe - Ic = gm
| . .
| . .
| . .
| . .
Ic_q+--------------..
| .. |
| . . |
| . . |
| . . |
|. . |
| . |
+---------------+------------- Vbe
Vbeq

Pretty simple really. No wonder I was so bored and fell asleep in EDSN101.

Paul Burridge wrote:
On Wed, 10 Sep 2003 10:25:49 +0100, "Kevin Aylward"
wrote:


That is, to achieve linear multiplication by this transistor gm
method, it necessarily requires a non-linear relation between I and
V for the transistors gm characteristics. This forms a proof of my
statement that the class A modulator achieves such modulation by a
non-linear process.

gwhite:

Please do not respond if you are going to past masses of waffle text
that you don't understand. Provide a *mathematical* *explicit*
disproof of my mathematics or present your retraction.

Well this is compelling stuff, I must say. I'd hoped to be able to
disappear on holiday for a week and return refreshed, but it looks
like I'm going to have to seek out cybercafes to keep up to date on
these exchanges instead. :-( Still no outright winner so far...

Not to me aint. The case is closed.

The problem with gwhite, is that his arguments are all based on "an
appeal to authority", and we all know that is not the way science is
done. He pastes reams of stuff without the slightest idea of what the
documents are talking about. The assumption being that such documents
back him up. They don't. He hasn't presented one, not even one
derivation of his claim, only end results. This is typical of all
vacuous claims. It says so in the bible, so it must be true sort of
thing.

On the otherhand, he does have a very valid point that one, could in
principle, make a modulator that does not depend on an inherent
non-linearity, he just happened to pick the wrong examples, and the
wrong person to debate with. He obviously learnt the basic concept from
a coarse he took, but never understood
enough to know when and how to apply it. For the active bipolar or fet
case, the gain setting is gm based, and this gm is electrically
controlled by the value of its
own current, hence, as a I proved, must have a non-linear V/I curve.
However, for example, in a passive case, things are different. If one
used a fet as a passive voltage controlled resister, the resistance is a
function of the gate source voltage, but the control voltage is not
connected accross the controlled resistance, and the resistance
variation is not implied to be a function of its own current, therefore
a non-linear resistance is not implied. Indeed, this technique is used
in guitar phaser pedals to produce a swept notch filter, and I designed
and built my
first one of those around 25 years ago, based on this concept. To make
the fet even more linear, as qwhite correctly suggested, I used, as is
well known standard practice, a series gate resister and feedback
resistor from drain to gate. Unfortunately, I made a mistake...in my
"there is only a world market for 5 computers" statement, I forgot what
I already knew:-)

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.