An Error Bound Particle Swarm Optimization for Analog Circuit Sizing

Abstract

An Error-Bound Particle Swarm Optimization (EB-PSO) is proposed in this work. The objective function is evaluated for each particle in each iteration. The velocity update equation is modified by introducing two new parameters ζ 1 and ζ 2 . These parameters varies exponentially, within the bounds (ζ 1,min , ζ 2,min ) and (ζ 1,max , ζ 2,max ), with respect to the number of iterations. Initially, a higher value of ζ 2 and minimum value of ζ 1 is chosen to facilitate a global search. Once the global error (ε 2 ) is less than the desired value, ζ 1 is allowed to increase from its minimum value and ζ 2 is held constant at ζ 2,max . This leads to local exploitation of the search space. The proposed algorithm is implemented on Python platform. To verify the effectiveness of the proposed EB-PSO algorithm in analog circuit sizing, a case study on the performance and optimization of two-stage op-amp is presented, whose validation is done in Cadence-Virtuoso environment at 45-nm CMOS technology. The results show that the proposed EB-PSO algorithm converges in 11 iterations for two-stage op-amp, whereas it takes 23, 29, and 41 iterations to converge for conventional GA, DE, and PSO algorithms respectively. INDEX TERMS Analog circuit sizing, Particle swarm optimization (PSO), constrained optimization.