[sdiy] Spice simulation of diff amp

[ASSI]

On Tuesday 11 February 2014, 10:27:36, Andrew Simper wrote:
> I have been researching manufacturing mismatch for some time. Certain
> simulators have a randomiser built in which applies noise to the model
> parameters and can show multiple plots to show the variation. The
> filter designer link that was recently posted has this feature. There
> is also an "area" parameter I know that Qucs has (and possibly more
> simulators?), which modifies multiple parameters at once. Neither of
> these approaches is actually going to simulate manufacturing variation
> that well, but they are good starting places.

They are actually quite useless if you really care about quantitative 
effects of manufacturing variation and don't just want to know how robust 
your design is to unspecified parametric variation (which could turn out 
both too big or small; also often some of the variations that are simulated 
that way aren't physically realizable).  On another tangent, if you're 
trying to get random variables in multiple dimensions, you'll need a really 
good random number generator or your sampling of the parameteric space will 
be patterned, leading to similar spurious patterns in the results.  If you 
also need non-uniform or non-normal distributions or (possibly non-linear) 
correlations between variables things get interesting real fast.

[dissertation]
> Which splits things up into different geometrically and spatially
> derived variations which intuitively seems like the correct approach
> and the actual variations measured look good when compared to real
> world examples show in the paper.

This is one of the ways to do the statistical equivalent of "small-signal 
analysis" or linearisation.  It works well enough for matching when you can 
assume the disturbance to be normal distributed with low variance compared 
to the base variable, not so well for other types of distributions.  A 
variance that is a function of some other variable (which is quite common in 
reality) and linear correlations can be accommodated with some more effort, 
but that also has limits.

> Using these types equations and
> Quc's inbuilt function specifications you could generate multiple
> spice parameters and have a look at the results, although this will
> take a long time since you'll need to define every device you want to
> randomise with a set of functions like this, so lots of copy and paste
> and editing and room for error.

Keep in mind that the dissertation you've linked to really only applies to 
integrated devices, not discretes.  That said, the basic problem with almost 
all SPICE models is that they have non-physical parameters and/or "physics-
based" parameters that are non-predictive (i.e. you may need to change other 
model parameters for regaining consistency).  The result is that even if the 
original model was perfectly accurate for the nominal device (which it never 
is), each variation gives you another device that you will never encounter 
in reality.  To determine how far from reality exactly is left as an 
exercise for the student.

As Douglas N. Adams said: "almost, but not quite, entirely unlike tea" even 
though he probably didn't have modeling in mind; also Norbert Wiener and 
Arturo Rosenblueth: "The best material model for a cat is another, or 
preferrably the same cat."


Regards,
Achim.
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