Globally Reliable Variation-Aware Sizing of Analog Integrated Circuits via Response Surfaces and Structural Homotopy

Abstract—This paper presents SANGRIA, a tool for automated globally reliable variation-aware sizing of analog integrated cir-cuits. Its keys to efficient search are adaptive response surface modeling, and a new concept, structural homotopy. Structural homotopy embeds homotopy-style objective function tightening into the search state’s structure, not dynamics. Searches at sev-eral different levels are conducted simultaneously: The loosest level does nominal dc simulation, and tighter levels add more analyses and {process, environmental} corners. New randomly generated designs are continually fed into the lowest (cheapest) level, always trying new regions to avoid premature convergence. For further efficiency, SANGRIA adaptively constructs response surface models, from which new candidate designs are optimally chosen according to both yield optimality on model and model prediction uncertainty. The stochastic gradient boosting models support arbitrary nonlinearities, and have linear scaling with input dimension and sample size. SANGRIA uses SPICE in the loop, supports accurate/complex statistical SPICE models, and does not make assumptions about the convexity or differentiability of the objective function. SANGRIA is demonstrated on four different analog circuits having from 10 to 50 devices and up to 444 design/process/environmental variables. Index Terms—Analog, design automation, integrated circuit, process variation. I