Mathematical Circuit Root Simplification Using an Ensemble Heuristic–Metaheuristic Algorithm

Symbolic pole/zero analysis is a crucial step in 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. This study presents a mathematical model combined with a heuristic–metaheuristic solution method for symbolic pole/zero simplification in operational transconductance amplifiers. 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 used for the simplification of the derived symbolic roots. The developed method is tested on three operational transconductance amplifiers. The obtained results show the effectiveness of the proposed method in achieving accurate simplified symbolic pole/zero expressions with the least complexity.