The ever increasing pace of analog IC design demands efficient means of automated design and optimization. Especially important is robust design. Its goal is to produce circuits whose behaviour stays within some predefined range when the manufacturing process variations and environmental effects remain bounded. Most of the design process 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 constrained optimization problem by means of penalty functions. We illustrate the method on a robust differential amplifier design problem. The resulting circuits show that a computer not only can improve circuits designed by humans, but is also capable of designing a circuit with very little 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.

In this paper, a method for nominal design of analog integrated circuits is presented that includes process variations and operating ranges by worst-case parameter sets. These sets are calculated adaptively during the sizing process based on sensitivity analyses. The method leads to robust designs with high parametric yield, while being much more efficient than design centering methods.