Defining Cost Functions for Robust IC Design and Optimization

The ever increasing pace of analog IC design demands efficient means of automated design and optimization. Es-pecially important is robust design. Its goal is to pro-duce circuits whose behaviour stays within some predefined range when the manufacturing process variations and envi-ronmental effects remain bounded. Most of the design pro-cess is still handled by IC designers manually. We present a simple mathematical formulation of the robust design and optimization problem and its transformation into a con-strained optimization problem by means of penalty func-tions. We illustrate the method on a robust differential am-plifier design problem. The resulting circuits show that a computer not only can improve circuits designed by hu-mans, but is also capable of designing a circuit with very lit-tle initial knowledge. Optimization runs resulted in circuits with similar or even better performance when compared to humanly designed circuits. The method can take advantage of parallel processing, but is still efficient enough to be run on a single computer. 1