Improvements to Statistical Characterization and Modeling, and a Caution to be Aware of Spurious Correlation in Statistical Simulation

This article presents two improvements to, and a warning about a previously unrecognized issue with, statistical modeling, characterization, and simulation. We focus on mismatch, which is key for analog IC design, but the topics addressed are generic. For relative variation (i.e., % difference), we show that conventional measures have significant issues when the variation is large. We present two new measures of % difference between <tex-math notation="LaTeX">y₂ </tex-math> and <tex-math notation="LaTeX">y₁ </tex-math> and show that <tex-math notation="LaTeX">100 · ln (y₂ / y₁) </tex-math> is the only measure that is physically correct for mismatch. We review existing, but not widely known, robust alternatives to the textbook approach to estimate standard deviation, show the limitations of these, and propose a new method that is intermediate between, and overcomes limitations of, the textbook and robust approaches. We then show how the accuracy of mismatch simulation, critical for analog IC design, is affected by “spurious correlation” between statistical samples; we are not aware that the importance of this has been recognized previously.