Nature inspired algorithm based design of near ideal fractional order low pass Chebyshev filters and their realization using OTAs and CCII

Abstract

Fractional order filters offer greater freedom of design and a precise control over stopband attenuation in electronic circuits and systems. This paper presents the design of a fractional order low pass Chebyshev filter (FOLCF) that achieves near-ideal response characteristics. The methodology introduced utilizes metaheuristic optimization methods, including particle swarm optimization, firefly algorithm, and grey wolf optimization. These techniques are employed to precisely adjust the filter coefficients for the orders (1+α), (2+α), and (3+α). The adjustment is carried out by comparing the desired behaviour of the FOLCF with generalized fractional order low pass transfer functions. Throughout these instances, the parameter α is varied within the range of (0, 1). The designed filters are then tested and compared on the basis of various factors. Simulation results demonstrate that the designed filters closely follow the behaviour of an ideal Chebyshev filter with maximum passband and stopband magnitude errors being −31.93 dB and −52.74 dB respectively for (1+α) order filters. These values for (2+α) and (3+α) order FOLCF have been observed to be −30.04 dB and −55.91 dB; −17.72 dB and −49.52 dB respectively. Furthermore, it has been observed that the proposed work outperforms existing state-of-the-art approaches in various aspects, including magnitude error, stopband attenuation, and cut-off frequency. The stability of the designed filters has been verified through stability analysis. Additionally, practical feasibility of the proposed FOLCF is demonstrated through SPICE simulations for α = [0.2,0.5,0.8] using second generation current conveyor (CCII) and operational transconductance amplifier (OTA) based topologies while approximating the constant phase element using fifth order continued fraction expansion. The SPICE implementations closely follow the behaviour of ideal filter with −48.67 dB and −62.8 dB as mean square errors for CCII and OTA circuits respectively, showcasing the proposed filters' superiority and practical applicability in advanced electronic design.