# Applying design equations in particle swarm optimization for auto-sizing of multi-stage opamps: an experimental study

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## Abstract

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.

## Keywords

Auto-sizing Design equation Genetic algorithm (GA) Multi-stage opamp Operational amplifier (opamp) Particle swarm optimization (PSO) Relaxation iteration (RI)## Notes

### Acknowledgements

This research was supported by the National Natural Science Foundation of China (NSFC) under the Grant Nos. 61474145 and 61974087.

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