gwhite wrote:
Frank Raffaeli wrote:

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

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

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

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


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

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

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

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

Kevin Aylward

http://www.anasoft.co.uk
SuperSpice, a very affordable Mixed-Mode
Windows Simulator with Schematic Capture,
Waveform Display, FFT's and Filter Design.