RadioBanter - RF amps: tuned load in Class A?

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Roy McCammon

September 10th 03 12:18 AM

Kevin Aylward wrote:

And to Roy, it occurred to me that you may have misunderstood my comment
on "women selects", I was of course, meaning selects to have sex with,
not as a long term partner.

I was distinguishing between "selects to have sex with"
vs "selects to get pregent by"

Roy McCammon

September 10th 03 12:18 AM

Paul Burridge

September 10th 03 12:21 AM

On Tue, 9 Sep 2003 09:13:49 +0100, "Kevin Aylward"
wrote:

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.

Not quite. She's out of the game for considerably more than 9 months
and not only that, she's run off her feet nurturing for years to come.
Consider the disparity in investment:
Male: 15 minutes 'work-ouk' producing two teaspoons of semen. Total
cost to male: the semen that would be naturally lost anyway, plus
maybe having to forego the time to down half a pint of beer with his
chums in the local pub.

Female: 9 months carrying, physical disfigurement, much physical pain
and then she's lumbered with a unceasingly demanding child who keeps
her from doing anything else than looking after it, morning noon and
night for years to come. Opportunity cost: work it out for yourself
but it's *enormous*. She's choosy because her investment into the
project is vast and has to be worth it in the long term. He's not
because his investment is negligable. Anything in a skirt will
suffice, particularly after a few beers.

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.

I'm not sure I understand you fully here. Some of your above remarks a
a bit disjointed. If you can re-phrase it to make more sense I'll try
and tackle this paragraph before I have to jet-off 2morrow.

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.

No thanks. It's *she* who'd have to be bloody well-off. I'm rather
fussy, I'll have you know.
But I'd agree that physical appearance is the single most significant
aspect with the accent on *single* and probably has been for all time
so far as the human race is concerned.
Shows of wealth are often a bit misleading. Wimmin do find them highly
attractive. But the reason they *think* they find them attractive
(nice house, nice holidays, nice car etc) and not the same as the
*real* reason they do, which is simply their genes trying to ensure
for themselves that the mate in question will be able to give the
offspring the best possible shot at life: better diet, better
schooling, better upbringing, better adult prospects of that offspring
attracting a similarly classy mate for him/herself.

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?

Straying too far off the subject for too long, Kev. I'm familiar with
Albert's work, too. And all the others of his ilk that were kicking
around in the early years of the 20th Century. Can't afford to get
bogged down in yet another off-topic discussion on the net. This
little excursion into human nature is taking the **** as it is.
Remember this is supposed to be an electronics design group!

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

I should only have to read your postings *once* m8. If you took more
trouble with your spelling, grammar and phraseology, these frequent
accusations you make about others' failing to understand you would
take up a good deal less of your time.

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.

Whatever. In any event I have no wish to **** decent people off by
making a habit of this kind of unfortunate off-topic exchange.

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 pressure from the PC brigade in the writer's mind must always be
considered when reading these kind of books. It's outrageous that some
ingorant pigs appear to take the view that their own personal
prejudices (like for a more equal world) should take precidence over
Truth. :-(

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'm not like most other men so kindly don't judge me in such crude
terms.

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/ ?

I'm sufficiently aware of the concept not to need to. In any event,
there are staggering numbers of fools wherever one looks in everyday
life without having to seek them out on the 'net to add to one's woes
over the state of humanity.

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

Generally good, of course. A few exceptions for pop stars, writers,
actors and artists, though.

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.

Well maybe you've finally explained with reasonable clarity what you
were struggling to explain earlier. If you'd now agree with me that
the charitable types, in the main, *believe* they are genuinely giving
something away to a worthy cause at a net cost to themselves, out of
the kindness of their hearts, then maybe we can at last say we've
found some common ground!
Let's hope so! :-)

--

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

Paul Burridge

September 10th 03 12:21 AM

gwhite

September 10th 03 02:45 AM

Kevin Aylward wrote:

gwhite wrote:

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.

Once again, it is *not* the non-linear aspect of it that "produces" the
multiplication (frequency translation in this case).

Maybe this will help you:

The Circuits and Filters Handbook
0849383412
CRC Press (c) 1995
Wai Kai Chen - Editor in Chief

Transconductance Multipliers

A direct, straightforward technique to realize the multiplication
function exploits the possibility of controlling the transconductance
of transistors through an electrical variable (current or voltage).
Although this feature is exhibited also by unilateral amplifiers,
most practical realizations use differential amplifiers to reduce
offset problems and enhance linearity [25]. Figure 32.32 shows a
generic schematic for a differential amplifier, consisting of two
identical three-terminal active devices with common bias current.
The expressions on the right display its associated transconductance
characteristics for npn-BJTs and n-channel MOSTs, respectively [25].
These characteristics are approximated to a first-order model as

i_y*v_x
i_z ~ --------- (BJT), i_z ~ sqrt(Beta*i_y)*v_x (32.39)
4*U_t

[~ := "approx. equal to"]

which clearly displays the multiplication operation, although restricted
to a rather small linearity range. Practical circuits based on this idea
focus mainly on increasing this range of linearity, and follow different
design strategies. Figure 32.33 shows an example, known as the Gilbert
cell, or Gilbert multiplier [23]. Corresponding realizations using MOS
transistors are discussed in [2] and [53]. Sanchez-Sinencio et al. [61]
present circuits to realize this multiplication function using OTA blocks.
On the other hand, [17] presents a tutorial discussion of different
linearization techniques for MOS differential amplifiers.

There you have it. For the BJT, i_z is linear according to i_y or v_x.
That is, you change v_x by 1 dB and the ouput changes by 1 dB provided
the coefficient for v_x (which is i_y) is not zero (vice versa for i_y
too). Note all the talk about linearity from the circuits perspective:
'...enhance linearity," and "although restricted to a rather small
linearity range," and "Practical circuits based on this idea focus mainly
on increasing this range of linearity," and "...a tutorial discussion of
different linearization techniques." So explicitly again: *non-linearity
is not required or even wanted for this particular multiplying function*.
The circuits perspective of linearity is consistant with the Signals and
Systems perspective. That some engineers don't know the definition is
notwithstanding.

The following from Lathi may help get you up to speed on the linearity
property:

SIGNALS, SYSTEMS AND COMMUNICATION
B. P. LATHI
Copyright © 1965 by John Wiley & Sons, Inc.
Library of Congress Catalog Card Number: 65-22428
SECOND CORRECTED PBINTINC, SEPTEMBER, 1967

pp2-4
+----------+
| |
f(t) O----+ A system +----O r(t)
| |
+----------+
Figure 1.1

1.1 PROPERTIES OF LINEAR SYSTEMS

For every system there is an input signal (or driving function) and an
output signal (or response function) (Fig. 1.1). A system processes the
input signal in a certain fashion to yield the output signal. The word
linear at once suggests that the response of a linear system should change
linearly with the driving function (note that this is not the same as saying
that the response should be linearly proportional to the driving function,
although this is a special case of linearity); that is, if r(t) is the response
to f(t) then kr(t) is the response to kf(t). Symbolically, if

f(t) - r(t)
then kf(t) - kr(t) (1.1)

The linear system, however, implies more than Eq. 1.1. We define a
linear system as a system for which it is true that if r1(t) is a response to
f1(t) and r2(t) is a response to f2(t) then r1(t) + r2(t) is a response to f1(t)
+ f2(t), irrespective of the choice of f1(t) and f2(t). Symbolically, if

f1(t) - r1(t)
f2(t) - r2(t)
then f1(t) + f2(t) - r1(t) + r2(t) (1.2)

Equation 1.2 actually expresses the principle of superposition symbolically.
Thus linear systems are characterized by the property of superposition.
We may consider Eq. 1.2 as the defining equation of a linear system;
that is, a system is linear if and only if it satisfies Eq. 1.2, irrespective
of the choice of f1(t) and f2(t).
Sometimes the condition is stated in the form,

a·f1(t) + b·f2(t) - a·r1(t) + b·r2(t) (1.3)

irrespective of the choice of f1(t), f2(t) and constants a and b. This will be
seen to be exactly equivalent to Eq. 1.2. Note that Eq. 1.2 is stronger
than and implies Eq. 1.1.

1.2 CLASSIFICATION OF LINEAR SYSTEMS

Linear systems may further be classified into lumped and distributed
systems. They may also be classified as time-invariant and time-variant
systems. We shall briefly discuss these classifications.

Lumped and Distributed Systems

...

Time-Invariant and Time-Variant Systems

As already mentioned, linear systems can also be classified into time-
invariant and time-variant systems. The systems whose parameters do
not change with time are called constant-parameter or time-invariant
systems. Most of the systems observed in practice belong to this category.

O---- L -----+
------+ |
f(t) | R(t)
-i(t)-+ |
O------------+
Figure 1.2

Linear time-invariant systems are characterized by linear equations
(algebraic, differential, or difference equations) with constant coefficients.
Circuits using passive elements are an example of time-invariant systems.
On the other hand, we have systems whose parameters change with time
and are therefore called variable parameter or time-variant (also time-
dependent) systems. Linear time-variant systems are characterized by
linear equations with time-dependent coefficients in general. An example
of a simple linear time-variant system is shown in Fig. 1.2. The driving
function f(t) is a voltage source applied at the input terminals of a
series R-L circuit where the resistor R(t) is a function of time. The
response is the current i(t). Note that the principle of superposition
must apply for a system to qualify as a linear system whether time-
variant or time-invariant. The reader may convince himself that
the system shown in Fig. 1.2 is a linear system. A linear modulator is
another example of linear time-variant system. In this ease the gain of
the modulator is proportional to the modulating signal.
The system characterized by Eq. 1.4

d^2r dr
---- + a·-- + b·r = f(t) (1.4)
dt^2 dt

is a linear time-invariant system, whereas the system characterized by
Eq. 1.5

d^2r dr
---- + -- + (2·t + 1)·r = f(t) (1.5)
dt^2 dt

is a linear time-variant system. Note that both these systems satisfy the
principle of superposition. This can be easily verified from Eqs. 1.4
and 1.5.
It is evident that for a time-invariant system if a driving function f(t)
yields a response function r(t), then the same driving function delayed by
time T will yield the same response function as before, but delayed by
time T. Symbolically, if

f(t) — r(t)
then f(t-T) - r(t-T) (1.6)

This property is obvious, in view of the time invariance of the system
parameters. Time-variant systems, however, do not in general satisfy
Eq. 1.6.

Some of Lathi's key statements with regard to this thread a
1. "... note that this is not the same as saying that the response should
be linearly proportional to the driving function, although this is a
special case of linearity"
2. "Linear systems may further be classified into lumped and distributed
systems. They may also be classified as time-invariant and time-variant
systems."
3. "...linear systems can also be classified into time-invariant and time-
variant systems"
4. "Linear time-variant systems are characterized by linear equations with
time-dependent coefficients in general."
5. "A linear modulator is another example of linear time-variant system.
In this ease the gain of the modulator is proportional to the modulating
signal."

Note that these remarks are from pp2-4 of text for a BS level course in the
EE curriculum. You can't get more basic than that.

With regard to #4 & #5 specifically, the following is a linear system with
time dependent coefficients *and* is also a "linear modulator":

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

I used this example early on to emphasize the points of #4 & #5. I made
it as simple as I could think of for the purpose of making it simple for
you -- all to no avail. After all this work, I really hope you finally
"got it," because if you have not, I am done helping.

~~~~~~~~~~~~~~~~~~~~~~~~

"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." -- Kevin Aylward

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

But the worm does turn:

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.

I see you are finally coming around, or maybe. One can never be too sure.

This is trivially obvious, and was
what I showed in my original analysis, gm is
inherently a small signal property.

Yes, and it is all you need for "multiplication." Your original claim
that "non-linearity" was "required" for multiplication was false, as
I wrote some 10,000 or so words ago.

Back and forth,... you are all over the map.

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.

Doesn't matter. Non-linearity is not required for the modulation to occur
and that is what started you out on your march. You said it was, you
were wrong.

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, ...

You are squirming. That "nothing is perfectly linear" is irrelevent.
Linear circuits are popular and much work goes into making non-ideal
(in the sense of being non-linear) devices appear as linear as possible.
Finally, the non-linear aspect (although ever present in some amount) is
not requisite for modulation to occur. If anything is trivally obvious
it should be that no device is a perfect ideal in *whatever* manner ideal
has been defined.

I claim that all practical devices have a non-linear
transfer function, ...

That is not now, nor has it ever been under contention.

...and it is this transfer function that results in
multiplication.

Well it can... sure. That is not now, nor has it ever been under
contention. But it is not *only* that aspect that can produce the
multplication. The actual configuration can use the first order terms
*alone* to acheive the multiplication.

To the extent the original circuit was non-linear, it was not that
non-linear aspect that was needed or even desired to produce the
modulation. In fact, a lot of work goes into linearizing the
transfer characteristic rather than the opposite. That the LO or
carrier port of the circuit can be driven Class C or D is
notwithstanding: that non-linear aspect is not inherently needed
for the modulation to occur. It exists more as an annoying non-
ideality that simply must be acknowledged and then mitigated in
many modulation applications.

The reason for Class C or D is for efficiency, as I wrote long ago.
The amp is not Class C or D "so that the modulation will occur."
In fact, the point is to find out how Class C or D can be used and
still achieve the desired effect. For tubes, that will likely be
plate modulation. The desire is for efficiency, and then to find
a way to make it work effectively. The point was not to "use Class
C or D so that modulation will occur."

I don't believe we are arguing about the same point.

Dude, it is pretty straightforward stuff. If you don't know what
is under discussion you might want to think before you write how
stupid someone else is.

I have better things to do.

Gee, thanks for making it so easy. So what if there are some
things you are shaky on? Get over it -- that is life. No one
knows everything.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
If gm(Vi) is represented by a Taylor expansion, any required terms
linear in Vi will integrate to Vi^2, that is

I = aV^2 + terms...

That is, the I verses V relation must be non-linear to achieve a gm that
is a function of voltage or current.

I don't know what your point was with all the gm stuff, but if you hook
it up like this:

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

....then the system is indeed a non-linear one [y(t) = x(t)^2].
This squaring function is a perfect example of why I wrote a long
time ago: "'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."

It takes a lot of work for designers to produce linear characteristics
in their linear multipliers. They like to draw straight and long lines
on their z = x·y graphs. That one non-linear operation is cleverly used
to cancel another (and get those nice long straight lines) is a design
detail. The bottom line is the end linearity, the linearity they use as
a selling point.

From AN-531
The analysis of operation of the MC1496 is based on the
ability of the device to deliver an output which is proportional
to the product of the input voltages V_x and V_y. This holds true
when the magnitudes of V_x and V_y are maintained within the
limits of linear operation of the three differential amplifiers in
the device. Expressed mathematically, the output voltage
(actually output current, which is converted to an output
voltage by an external load resistance), V_o is given by

V_o = K·V_x·V_y (1)

.... The MC1595 multiplier contains the basic circuit configuration
of the MC1496 plus additional circuitry which results in linear
multiplier operation over a large input voltage range.
....
Figure 3 shows the MC1496 in a balanced modulator
circuit operating with +12 and –8 volt supplies. Excellent
gain and carrier suppression can be obtained with this circuit
by operating the upper (carrier) differential amplifiers at a
saturated level and the lower differential amplifier in a linear
mode...
Operating with a high level carrier input has the
advantages of maximizing device gain and insuring that any
amplitude variations present on the carrier do not appear on
the output sidebands. It has the disadvantage of increasing
some of the spurious signals...
[Saturation has nothing to do with the multiplication function.
In fact the extra non-linearity has the caveat of spuroius products.]
....
Operation with the carrier differential amplifiers in a
linear mode theoretically should produce only the desired
sidebands with no spurious outputs. Such linear operation is
achieved by reducing the carrier input level to 15 mV rms or
less.
This mode of operation does reduce spurious output
levels significantly...
[Again, non-linear operation is not required to produce the
modulation. In fact, it reduces spurious products that would
otherwise need filtering, if possible.]

And it goes on and on and on and on. Linear means linear.
Get over it.

gwhite

September 10th 03 02:45 AM

Kevin Aylward

September 10th 03 09:09 AM

Russell Shaw wrote:
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)

I have already pointed out the light dependant resistor in another post
in this thread, so I did already do a retraction and a qualification on
this point. This was a minor oversight. The distinction is whether or
not the controlling elements output terminals are connected to its
controlling terminals. If the controlling terminals, are connected to
the controlled terminals then we have a non-linear resister de-facto. A
resister can only be linear if its resistance does not depend on the
current through it, or the voltage across it.

In the case of the transistor, the gain is set by its small signal
resistance re=1/gm. However, the control of the value of gm is by its
own current, therefore it has to be non-linear.

An easy way to see this is the transistor is equivalent to a voltage
being applied across a resister re. Make the voltage a sine wave. Now
apply an additional current through the resister. If the resister was
linear, only an additional fixed dc current would flow, the peak to peak
value of the sine wave would not change.

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 10th 03 09:09 AM

Kevin Aylward

September 10th 03 10:25 AM

gwhite wrote:
Kevin Aylward wrote:

gwhite wrote:

Once again, it is *not* the non-linear aspect of it that "produces"
the multiplication (frequency translation in this case).

Indeed it is, in the case of the bipolar or fet multiplier, I proved it
mathematically. Unfortunately it appears you cannot understand the
proof. See below for a more exact analysis.

Maybe this will help you:

{snip ramblings}

Nope.

~~~~~~~~~~~~~~~~~~~~~~~~

"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." -- Kevin
Aylward

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

I retracted this in the pure technical sense. I restricted the claim to
electrical connected, real devices. However, this statement was made in
support of my fundamental claim that the Class A amp you presented
achieved multiplication specifically because of its non-linear transfer
function due to the diode equation. I stand by that claim, which is the
one that matters for this discussion. I have proved this, as an
extension to my prior diode presentation, in detail below.

But the worm does turn:

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.

I see you are finally coming around, or maybe. One can never be too
sure.

Nope. I was trying to give you your due on some points.

This is trivially obvious, and was
what I showed in my original analysis, gm is
inherently a small signal property.

Yes, and it is all you need for "multiplication." Your original claim
that "non-linearity" was "required" for multiplication was false, as
I wrote some 10,000 or so words ago.

You shouldn't have bothered, it was much wasted much effort. I
mathematically proved that the diode has to have a non-linear transfer
function in order to obtain a gm that varies with a control signal, and
thus achieve multiplication.

The fact that you are unable to explicitly, understand, discuss and
refute that proof on mathematical points says much about your ability
and credibility.

Back and forth,... you are all over the map.

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.

Doesn't matter. Non-linearity is not required for the modulation to
occur and that is what started you out on your march. You said it
was, you were wrong.

Nope. I am correct. I prove it below. Excluding, my retraction of the
ideal, unavailable VRC, or the light bulb and light dependant resister,
where the controlled terminals are not connected to the controlling
terminals. This was a minor slip-up as I was implicitly referring to
transistor type circuits. I regret not being more precise, but nobody's
perfect.

...and it is this transfer function that results in
multiplication.

Well it can... sure. That is not now, nor has it ever been under
contention. But it is not *only* that aspect that can produce the
multplication. The actual configuration can use the first order terms
*alone* to acheive the multiplication.

Not in the transistor case it can't. I have proven otherwise. All you
are doing here is throwing away non-linear terms after the fact. This
dose not mean that non-linear terms are not required in order to achieve
the final linear result.

Cut the bull****, and show me an actual mathematical derivation
supporting your view, rather than quoting end results from books you
don't understand.

To the extent the original circuit was non-linear, it was not that
non-linear aspect that was needed or even desired to produce the
modulation.

I have mathematically proved otherwise. Refute my proof by a
mathematical argument or retract your claims.

In fact, a lot of work goes into linearizing the
transfer characteristic rather than the opposite.

Yeah... and I don't know this...get real. What part of "I have been a
successful analogue design engineer for over 20 years" do you fail to
understand.

That the LO or
carrier port of the circuit can be driven Class C or D is
notwithstanding: that non-linear aspect is not inherently needed
for the modulation to occur. It exists more as an annoying non-
ideality that simply must be acknowledged and then mitigated in
many modulation applications.

{snip more waffel}

I don't believe we are arguing about the same point.

Dude, it is pretty straightforward stuff.

Indeed it is. Stuff that you have missed by not doing the actual
details. You made a simple mistake. Live with it.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~
If gm(Vi) is represented by a Taylor expansion, any required terms
linear in Vi will integrate to Vi^2, that is

I = aV^2 + terms...

That is, the I verses V relation must be non-linear to achieve a gm
that is a function of voltage or current.

I don't know what your point was with all the gm stuff,

I know you don't. Its quite sad really. You have no idea of electronic
circuits and are unable to do a derivation of the gain of an amplifier.
I honestly though you were sufficiently qualified to understand these
mathematical details, obvious I was wrong.

I am taking a guess here that you still wont understand my black and
white disproof of your claims, because you simple don't have the
mathematical competence to do so, nor the competence to understand that
you lack such competence.

but if you
hook it up like this:

Oh dear...

I showed that if gm = kVi., i.e. the required linear gm, then the only
way to achieve this was if its defining equation was non-linear. This is
because gm=dI/dv. Linear gm vith its own current controlling it,
inherently implies nonlineaity of the I/V graph. The fact that you
introduce some daft multiplier connected up as a squaring circuit shows
you just haven't got a clue.

{snip irrelevant}

Notes:
Vin1 is applied across an effective resistance re=1/gm. To get any gain
change gm,re must be a function of either the current or voltage i.e.
Vin2 or Ini2, in this case its the current though it. A resistance that
changes is value based on the current through it is necessarily a
non-linear resister. Its that simple.

{snip irelevent waffle}

Stop quoting text you don't understand. Show me real mathematical
derivations.

From AN-531
The analysis of operation of the MC1496 is based on the
ability of the device to deliver an output which is proportional
to the product of the input voltages V_x and V_y. This holds true
when the magnitudes of V_x and V_y are maintained within the
limits of linear operation of the three differential amplifiers in
the device. Expressed mathematically, the output voltage
(actually output current, which is converted to an output
voltage by an external load resistance), V_o is given by

V_o = K·V_x·V_y (1)

Get over it.

Err. where is your derivation of this equation? I wager if you could,
you would.

Let me do it for you.

The small signal output current of a transister amplifier is given by:

Iout = V1*gm

Where gm is the transister gm, and is given by, gm=d(Ie)/d(Vbe)

Ie is the emitter current, Vbe = V1 is the voltage across the base
emitter diode, and V1 is the input signal.

Now, please let me know where you disagree with any exact point.

I am now going to assume that the transistors gm is controlled by
another current I.

That is, gm = k.I

so that, from the above expression for Iout:

Iout = V1.k.I

That is, a linear multiplication of I and V1. All well and good so far.

However, we noted that

gm = dI/dV, so that we must have

k.I = dI/dV

or

dI/I = k.dV

and upon solving this differential equation, we obtain

I = c.exp(V.k)

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.

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 10th 03 10:25 AM

Kevin Aylward

September 10th 03 10:41 AM

Russell Shaw wrote:
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)

I have already pointed out the light dependant resistor in another post
in this thread, so I did already do a retraction and a qualification on
this point. This was a minor oversight. The distinction is whether or
not the controlling elements output terminals are connected to its
controlling terminals. If the controlling terminals, are connected to
the controlled terminals then we have a non-linear resister de-facto. A
resister can only be linear if its resistance does not depend on the
current through it, or the voltage across it.

In the case of the transistor, the gain is set by its small signal
resistance re=1/gm. However, the control of the value of gm is by its
own bias current, therefore it has to be non-linear.

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 10th 03 10:41 AM

Russell Shaw wrote:
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)

I have already pointed out the light dependant resistor in another post
in this thread, so I did already do a retraction and a qualification on
this point. This was a minor oversight. The distinction is whether or
not the controlling elements output terminals are connected to its
controlling terminals. If the controlling terminals, are connected to
the controlled terminals then we have a non-linear resister de-facto. A
resister can only be linear if its resistance does not depend on the
current through it, or the voltage across it.

In the case of the transistor, the gain is set by its small signal
resistance re=1/gm. However, the control of the value of gm is by its
own bias current, therefore it has to be non-linear.

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

September 10th 03 03:10 PM

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

September 10th 03 03:10 PM

Frank Raffaeli

September 10th 03 05:13 PM

"Kevin Aylward" wrote in message ...
Frank Raffaeli wrote:
"Kevin Aylward" wrote in message
...

[snipped much voluminous banter]

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.

[snipped more banter]

Does the above pose a question, or is it mere rhetoric? Could the
scientific method be applied with gusto? Are Win and Kev evenly
matched?

I don't know. How tall is he, I'm only 5'8"

All talk, then. Pity, I would have enjoyed the sport of a contest. It
seems this issue has been smothered with words. If one could apply the
"science" to "design", the words would have more meaning.

Frank Raffaeli
http://www.aomwireless.com/

Frank Raffaeli

September 10th 03 05:13 PM

Kevin Aylward

September 12th 03 07:50 AM

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

September 12th 03 07:50 AM

Kevin Aylward

September 12th 03 08:17 AM

Paul Burridge wrote:
On Mon, 08 Sep 2003 10:23:36 -0700, gwhite wrote:

That is clever -- you want me to "declare" something is true that
I've made no reference to. You are quite the inventor. Face it:
you had an incorrect notion about linearity. All the rest of your
words are twisting, squirming, and turning to try to save face after
you acted condescending (and still do) about a very simple matter.
That's all.

I have to say I've been wrestling with this attitude problem of kev's
as well. Earlier this evening I postulated to myself that the reason
for all these contradictory posts

What contradictory posts?

As far as attitude goes, I think we can all get rather exasperated when
someone else uses very strong rhetoric against ones own competence, when
it is trivially obvious that such claims are completely without any
merit whatsoever.

and arguments over semantics might
possibly be due to Kev's impared usage of English.

See below.

If the guy's
dyslexic or has some other comprehension problem, he might very well
be an electronics genius but we'd find it hard to tell because this
veil between he and us muddies the water both ways.

This makes little sense. Most of my posts are very clear, although not
necessarily pristine in all aspects of their structure. Any lack of
comprehension of them, is often a problem with the reader.

You view as
expressed above is a very much more cynical one, but I'm forming the
view that one or t'other must explain it. But Kev has admitted to
English not being his strong suit elsewhere on the group

My fundamental problem with English is that I have a very poor memory,
in conjunction with the fact that I am a two fingered typist. This
results in an inability to spell or type accurately. I usually function
by understanding and deriving results from basic concepts, rather than
by remembering millions of facts. Unfortunately I don't always check the
spell checked version that well. For instance, "simplely" might come out
as "simple" instead of "simply", making the statement "Its that simply",
grammatically wrong.

and if that's
the case and he really *does* know what he's talking about then

Of course I do.

I feel
sorry for him. It must be pretty ****ty and exceedingly frustrating
for anyone in that position. I know; I've met a few and it's ruined
their lives.

My life is quite fine thank you. I have wrote volumes of decent
technical reports, with no complaints.

I usually write quite accurately, expressing exactly what I want to say
in order to cover my arse. I do this explicitly, deliberately and
seriously as a general rule, with the method of "Yes Minister" TV series
speak. Often, it is a joy to watch other people fail to understand what
was actually said. For example, suppose the Minister had read a paper
indicating that a proposal of his would generate 500 redundancies. In
the House of Commons, he would say "No person informed me that there
would be any redundancies from my proposal". If you actually go back and
check my posts, you might be well surprised how subtle some of the
points are. Of course, at times I have made what might have been
inaccurate statements, but this is often simply because I have
temporally forgot something that I know well, or I have made an
assumption, that the obvious exceptions, are being deliberately ignored
for the purposes of the discussion. The issue here, is that the novice,
interprets this as a lack of understanding on my part. It just gets too
cumbersome addressing all the details, when only the general picture is
required.

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 12th 03 08:17 AM

gwhite

September 15th 03 05:02 AM

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.

gwhite

September 15th 03 05:02 AM

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