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 $\zeta _{1}$ and $\zeta _{2}$ . These parameters varies exponentially, within the bounds ( $\zeta _{1,min}$ , $\zeta _{2,min}$ ) and ( $\zeta _{1,max}$ , $\zeta _{2,max}$ ), with respect to the number of iterations. Initially, a higher value of $\zeta _{2}$ and minimum value of $\zeta _{1}$ is chosen to facilitate a global search. Once the global error ( $\varepsilon _{2}$ ) is less than the desired value, $\zeta _{1}$ is allowed to increase from its minimum value and $\zeta _{2}$ is held constant at $\zeta _{2,max}$ . 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.

Keywords

• Analog circuit sizing
• particle swarm optimization (PSO)
• constrained optimization