spectrallypure wrote:
> The more I ask about the infamous correlation parameter, the more
> astonished I get... Today I asked an associate professor, which I know
> has some experience in analog design (i.e. has done some working
> silicon), and he was totally surprised to learn about it... he had no
> idea of its existence!!!
>
> I have also searched in the do***entation of two other design kits
> besides AMS (namely, TSMC & UMC), and found no references whatsoever
> about how to take into account matched groups of transistors. I think
> these are rather well-known and widely-used processes, why does it
> seem nobody cared about do***enting the proper way of performing
> montecarlo simulations, taking into account matched pairs?
>
> ...I guess virtually everybody working in analog MUST do montecarlo
> simulations before going to fabrication, and MUST take into account
> matching on those simulations... How do they (properly) do it? :O
>
> Puzzled (and also desperate, but that's normal :-) ),
>
> Jorge.
Jorge,
The problem is not that complicated. Say you have two devices with a
parameter which is varying
randomly with a variance of s. Then the difference between the two devices
will be of
v(x-y)=2*v-2*cov(x,y)=2*v*(1-cc)
where cc is correlation coefficient. so if there's no correlation, the
variance of the difference
(mismatch) is sqrt(2) time larger than the variance of the individuals
(m=sqrt(2)*v). With a
non-zero correlation coeff., the variance of the difference is
sqrt(2)*sqrt(1-cc).
Therefore, by choosing an appropriate correlation coefficient, you can
obtain the desired mismatch
distribution. Say you want a resulting mismatch variance of w, you get cc
= 1 - 0.5*w/v = 1 -
sqrt(0.5)*v/m
As an example, say you have a differential pair and want to correlate the
two devices. First run a
simulation with two uncorrelated devices and from the results extract the
variance of the
parameter(s) you're interested into (drain current, threshold voltage,
transconductance, whatever).
Then, assuming you know what variance you *expect* for these parameters,
calculate the correlation
coeffs accordingly.
The real problem here is to accurately characterize the mismatch for a
given process, that is, to
know what to expect. If you know that, then your problem's solved.
Unfortunately accurate and
thorough mismatch data is not often available - it takes a lot of effort
and time to characterize a
process for mismatch - and you have no choice but to try and estimate it.
Mostly for mature
processes specifically dedicated to analog/rf applications you will find
good matching data, I guess.
Considering all these problems and the efforts it takes to predict
correlation coeffs for all the
matched devices in a circuit, and considering that this effort might quite
well be useless unless
you have a high confidence in your process and its data, it might be an
option to oversize a bit
your design. It will give you confidence and save you time and headache...
Just my two cents ;)
Cheers,
Stéphane
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