This paper presents stochastic convergence analysis of particle swarm optimization algorithm involving randomness and applying the results to the Analog RF Circuits to optimize the circuit parameters. In every iteration, each particle position is represented as vector and the standard particle swarm algorithm determined by positive real tipple {w,c 1 ,c 2 }. Comparisons for convergence are presented with respect to fixed tipple {w,c 1 ,c 2 } and random tipple {w,c 1 ,c 2 }. Various results show that the randomness in defining new position to particle leads to better convergence property. Also, exploration and exploitation trade off are discussed with examples. It is demonstrated that each particle undergoes both exploration and exploitation in convergence process; if the randomness in the particle generation is considered. The parameters considered for RF circuit are cutoff frequency, Phase Noise and Signal to Noise Ratio (SNR). Results are compared between both fixed values and random values of parameters in convergence analysis of PSO.