# Overview of IC Statistical Modeling

• J. C. Zhang
• M. A. Styblinski

## Abstract

Although the optimization problems introduced in the previous chapter can be formulated for any circuit, the methods for the problem solution strongly depend on the statistical properties represented by a suitable statistical model. At the circuit (simulator) parameter level, the circuit statistical model is determined by the transformation e i = e i (x, θ) and the p.d.f. f(θ). For the resistive voltage divider of Fig. 1.1, the statistical model can be stated as:
$$\left\{ {\matrix{ {{x_i}:{\rm{nominal element values}}} \hfill \cr {{\theta _i}:{\rm{element tolerances}}} \hfill \cr {{e_i} = {x_i} + {\theta _i},\,i = 1,2,} \hfill \cr {{\rm{or}}\,{e_i} = {x_i}\left( {1 + {\theta _i}} \right)\,{\rm{if}}\,{\theta _i}\,{\rm{has the relative tolerance fixed}}} \hfill \cr {{\theta _1}\,{\rm{and}}\,{\theta _2}\,{\rm{are statistically independent}}{\rm{.}}} \hfill \cr } } \right.$$

### Keywords

Diox Active Element