Predictable Equation-Based Analog Optimization Based on Explicit Capture of Modeling Error Statistics

Equation-based optimization using geometric programming (GP) for automated synthesis of analog circuits has recently gained broader adoption. A major outstanding challenge is the inaccuracy resulting from fitting the complex behavior of scaled transistors to posynomial functions. In this paper, we advance a novel optimization strategy that explicitly handles the error of the model in the course of optimization. The innovation is in enabling the successive refinement of transistor models within gradually reducing ranges of operating conditions and dimensions. Refining via a brute force requires exponential complexity. The key contribution is the development of a framework that optimizes efficient convex formulations, while using SPICE as a feasibility oracle to identify solutions that are feasible with respect to the accurate behavior rather than the fitted model. Due to the poor posynomial fit, standard GP can return grossly infeasible solutions. Our approach dramatically improves feasibility. We accomplish this by introducing robust modeling of the fitting error's sample distribution information explicitly within the optimization. To address cases of highly stringent constraints, we introduce an automated method for identifying a true feasible solution through minimal relaxation of design targets. We demonstrate the effectiveness of our algorithm on two benchmarks: a two-stage CMOS operational amplifier and a voltage-controlled oscillator designed in TSMC 0.18 μm CMOS technology. Our algorithm is able to identify superior solution points producing uniformly better power and area values under a gain constraint with improvements of up to 50% in power and 10% in area for the amplifier design. Moreover, whereas standard GP methods produced solutions with constraint violations as large as 45%, our method finds feasible solutions.