This paper presents an experimental study on using analytical design equations in the particle swarm optimization (PSO) for the automatic sizing of multi-stage operational amplifiers (opamps). Differing from the existing research, this work incorporates design equations in the PSO search process in attempt to reduce the search space dimensionality and the number of PSO iterations without sacrificing the quality of search results. Design equations are approximate characterization of the opamp performance metrics in analytical form, which are widely used in manual design process. However, the opamp device sizes cannot be uniquely solved from a set of design equations. Heuristic search can serve as a local optimizer in a reduced-dimensional search space to further refine optimization. Extensive simulation-based experimental PSO search results are presented to demonstrate the effectiveness of the proposed auto-sizing tactic. An alternative genetic algorithm based search method is implemented as well and tested for comparison.

本文提出了在粒子群优化（PSO）中使用解析设计方程式自动调整多级运算放大器（opamps）尺寸的实验研究。与现有的研究不同，这项工作在PSO搜索过程中纳入了设计方程，以尝试在不牺牲搜索结果质量的情况下减小搜索空间的维数和PSO迭代次数。设计方程式是分析形式的运算放大器性能指标的近似表征，在手动设计过程中被广泛使用。但是，不能从一组设计方程式中唯一求解运算放大器的尺寸。启发式搜索可以在降维搜索空间中充当局部优化器，以进一步优化优化。提出了基于模拟的广泛实验PSO搜索结果，以证明所提出的自动调整大小策略的有效性。还实现了基于替代遗传算法的搜索方法，并对其进行了测试以进行比较。