Vol.:(0123456789) 1 3 Evolutionary Intelligence https://doi.org/10.1007/s12065-020-00495-5 SPECIAL ISSUE Random ofset minimization in low frequency front‑end amplifers using swarm intelligence based techniques Naushad Manzoor Laskar 1  · Koushik Guha 1  · P. K. Paul 1  · K. L. Baishnab 1 Received: 24 June 2019 / Revised: 12 August 2020 / Accepted: 15 September 2020 © Springer-Verlag GmbH Germany, part of Springer Nature 2020 Abstract Random ofset in amplifers arises mainly due to random variations i.e. inherent mismatch in transistor parameters and greatly impacts its overall design specifcations, especially in case of low frequency application. It must be minimized for high precision in the amplifer’s performance. A new approach for minimization of random ofset voltage in amplifers has been proposed through the use of swarm intelligence based optimization algorithms due to their derivative free nature and easy search mechanism. The approach involves frstly, modelling the random ofset voltage due to mismatch between transis- tors parameters based on Pelgrom’s model and then minimizing the formulated model subjected to design constraints using swarm intelligence based algorithms. Two case studies are considered, frstly, a high swing Folded Cascode Operational Transconductance Amplifer (OTA) and secondly, a Recycling Folded Cascode (RFC) OTA. Comparative analysis have been performed by recording best, worst and mean data for 2500 function evaluations and also using statistical analysis such as Friedmann’s test and Mann–Whitney’s U test. The results indicate that the Hybrid Whale Particle Swarm Optimization (HWPSO) algorithm outperforms the other state of the art algorithms by giving a minimum random ofset voltage of 7.2 mV and 1.452 mV with a mean rank of 1.55 and 1.75 for the 1st and 2nd case studies respectively. Validation of HWPSO results have been done by performing simulations and Monte Carlo Analysis for the two amplifers in Cadence Virtuoso, which are found to be in close agreement with the algorithmic results. Keywords Random ofset voltage · Mismatch · Pelgrom’s model · Swarm based algorithms · Optimization · Monte Carlo analysis 1 Introduction An amplifer is an indispensable element in the front end design of any system [1] and should meet the minimum design specifcations required for optimal performance of the system [1, 2]. Ofset voltage is an important design specifcation in any amplifer design. A high value of ofset voltage is undesirable as it directly impacts the accuracy and precision of other design parameters such as gain, Common Mode Rejection Ratio (CMRR), noise etc. in the amplifer [3]. Especially in case of low frequency (< 20 kHz) systems such as in biomedical or neural amplifers, the signals them- selves are of low amplitudes (µV to lower mV range) and a high value of ofset voltage in such cases would lead to erroneous results in other design specifcations, thus afect- ing the precision of the design [4, 5]. So, minimizing the ofset voltages in such cases becomes even more important. Ofset Voltages are mainly of two types: Systematic Ofset and Random Ofset. Systematic Ofset arises mainly due to channel length modulation of transistors [6] and can be minimized by proper sizing of transistors and by adjusting the bias currents [7]. On the other hand, random ofset arises due to inherent mismatch of transistors and other device parameters [8] and is very difcult to handle. These random variations of parameters greatly infuences the precision of circuits and limits the performance. * Naushad Manzoor Laskar naushad.0015@gmail.com Koushik Guha koushikguha2009@gmail.com P. K. Paul pkp059@gmail.com K. L. Baishnab klbaishnab@gmail.com 1 Department of ECE, NIT Silchar, Silchar, Assam 788010, India