Analog layout retargeting using geometric programming

To satisfy the requirements of complex and special analog layout constraints, a new analog layout retargeting method is presented in this article. Our approach uses geometric programming (GP) to achieve new technology design rules, implement device symmetry and matching constraints, and manage parasitics optimization. The GP, a class of nonlinear optimization problem, can be transferred or fitted into a convex optimization problem. Therefore, a global optimum solution can be achieved. Moreover, the GP can address problems with large-scale variables and constraints without setting an initialization variable range. To meet the prerequisites of the GP methodology for analog layout automation, we propose three kinds of mathematical transformations, including negative coefficient transformation, fraction transformation, and maximum of posynomial transformation. The efficiency and effectiveness of the proposed algorithm, as compared with the other existing methods, are demonstrated by a basic case-study example: a two-stage Miller-compensated operational amplifier and a single-ended folded cascode operational amplifier.