Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

# Mathematical Root Simplification in Operational Amplifiers using an Ensemble Heuristic-Metaheuristic Algorithm

Version 1 : Received: 8 February 2023 / Approved: 9 February 2023 / Online: 9 February 2023 (11:08:12 CET)

A peer-reviewed article of this Preprint also exists.

Behmanesh-Fard, N.; Yazdanjouei, H.; Shokouhifar, M.; Werner, F. Mathematical Circuit Root Simplification Using an Ensemble Heuristic–Metaheuristic Algorithm. Mathematics 2023, 11, 1498. Behmanesh-Fard, N.; Yazdanjouei, H.; Shokouhifar, M.; Werner, F. Mathematical Circuit Root Simplification Using an Ensemble Heuristic&ndash;Metaheuristic Algorithm. Mathematics 2023, 11, 1498.

## Abstract

Symbolic pole/zero analysis is an important step when designing an analog operational amplifier. Generally, a simplified symbolic analysis of analog circuits suffers from NP-hardness, i.e., an exponential growth of the number of symbolic terms of the transfer function with the circuit size. In this study, we present a mathematical model combined with a heuristic-metaheuristic solution method for the symbolic pole/zero simplification in operational transconductance amplifiers (OTA). At first, the circuit is symbolically solved and an improved root splitting method is applied to extract symbolic poles/zeroes from the exact expanded transfer function. Then, a hybrid algorithm based on heuristic information and a metaheuristic technique using simulated annealing is performed for the simplification of the derived symbolic pole/zero expressions. The developed method has been tested on three analog OTAs. The obtained results show the effectiveness of the proposed method to achieve accurate simplified symbolic pole/zero expressions with the least complexity.

## Keywords

operational transconductance amplifiers; symbolic circuit analysis; pole/zero extraction; root splitting; simplification; simulated annealing

## Subject

Computer Science and Mathematics, Applied Mathematics