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