This work introduces a Partition Bound Particle Swarm Optimization (PB-PSO) algorithm to enhance convergence rates in analog circuit optimization. Two new parameters, ζ 1 and ζ 2 , are incorporated to adaptively update particle velocities based on iteration numbers. The parameter ζ 1 depends on the nonlinear convergence factor (α) and the number of iterations, N . The results indicate that ζ 1 's optimal value occurs with α = 4. ζ 2 partitions iterations into two regions, aiding local and global search. The PB-PSO algorithm, implemented in Python, demonstrates higher convergence rates than existing methods, with successful designs verified through Cadence-Virtuoso circuit simulations. The proposed PB-PSO algorithm converges in 15 and 13 iterations for differential amplifier and two-stage op-amp respectively. For a case study of two-stage amplifier, it achieves a gain of 60.4 dB with a phase margin of 79.76 • , meeting input specifications within constraints. The figure of merit was then evaluated using the obtained parameters, which turns out to be 0.275 V −2 . INDEX TERMS Particle swarm optimization (PSO), analog circuit sizing, low power, operational amplifiers, constrained optimization.