This paper presents an analysis of thermal noise of differential amplifier and automated sizing procedure with thermal noise incorporation, in addition to various design specifications, as constraints in the design process. Human behaviour-based particle swarm optimisation (HPSO), a swarm intelligence (SI)-based optimisation algorithm is used to perform the sizing task to obtain optimal value of design variables value subject to a satisfying set of constraints, with the main objective of designing a low-noise amplifier with minimum circuit area. The presented design procedure gives an option of considering both width and length of MOS transistor as design variables, which in turn can tune trade-off circuit performance parameters. The computational analysis is performed in MATLAB and CADENCE tool with UMC 180 nm parameters technology is used to validate the presented design procedure. Further, the performance of the purposed automated design methodology is compared with previous design methodology to check its efficiency in terms of speed, time and robustness.