Hello,

I've a question regarding capacitor matching that I'm sure you gurus will be able to answer!

Say I have an 11-b ADC but require only 10-b SNDR - I only need 10-b matching, correct?

So, say I have a capacitor of value 200fF. For plus/minus 3 sigma (total 6 sigma?), the standard deviation in monte carlo simulation should be (200fF/2^10)/3 = 0.065fF (should I be dividing by 6 here OR 3??). So over 3 sigma, the total would come to 3 times this, or 6 times this....?

Anyway. Supposed I run 100 monte carlos (how many are usually required, is there a way to calculate this?) and get the standard deviation (1 sigma) to be 0.09fF (picked out of thin air!). Obviously this wont do.

So the plan COULD be to use two 400fF caps in series to arrive at the 200fF -> with the increased area, this should help matching while still arriving at a low 200fF capacitance (so you CAN get good matching for lower value caps, the area just balloons). Anyway, suppose I run 100 monte-carlos on a 400fF cap and the standard deviation comes out to be 0.08fF.

This 0.08fF is still higher than 0.065fF, which is the value we require for 200fF 10-b matching. However, if we look at 10-b matching for the 400fF cap ((400f/2^10)/3 = 0.13fF) then this meets that requirement.

But HOW does this relate to the 200fF matching requirement that I need? I'm not understanding how these numbers fit together.
One last question - it seems as I increase area (and hence capacitance), the standard deviation goes up in absolute terms. However relative to the size of the cap the matching does improve - is this correct? So... if the deviation goes up in absolute terms it will never be lower than the 200fF standard deviation I require - so there must be some maths trickery somewhere. How do you calculate the standard deviation for a 200fF cap, implemented as two 400fF caps in series?

Of course I can put the two caps in series and find out the standard deviation from the calculator, but I guess my question is more about matching requirement, the maths behind it, and some confusion about 6 sigma!

Anyway, thanks for any help - much appreciated.