White Box Model of Feasible Solutions of Unity Gain Cells

Abstract

Equations or symbolic models of analog circuits increase designers' quantitative and qualitative understanding of a circuit, leading to a better decision-making. In this work symbolic regression is defined as white-box modeling, as opposed to other, more opaque, modeling types. This paper presents an approach to generate data-driven white box models. Our approach consists of two steps: firstly, the Pareto-optimal performance sizes of the Unity Gain Cell are obtained. For this work, unity gain and bandwidth have been simultaneously optimized using the NSGA-II algorithms. Secondly, the resulting Pareto Optimal front is used as data for the construction of white box models of performance as a function of the MOSFET design variables using Multigene genetic programming, which is a modified symbolic regression technique. Experiments were carried out using data obtained by SPICE simulation from the optimization of a voltage follower and a current follower, a set of nine functions (including operators), RMSE as precision measure, and a number of nodes as complexity measure. Among the symbolic models obtained, the simplest in terms of interpretability were sums of polynomials of the design variables. It was found that Multigene Genetic Programming can extract interpretable expressions even where the original design space was not sampled uniformly.