Optimization design of fractional‐order Chebyshev lowpass filters based on genetic algorithm
Xue Ting He, Zhizhong Hu
Abstract
Abstract Fractional‐order filters have received extensive attention from international scholars because of their greater design freedom and continuously stepped stopband attenuation rate. Based on genetic algorithm (GA), this paper proposes an optimum design approach for fractional‐order Chebyshev lowpass filters that meet design specifications. The fractional order and ripples attenuation of the normalized Chebyshev lowpass filter are calculated according to specifications, the integer order in the Chebyshev polynomial is replaced with the calculated fractional order, and then the fractional‐order Chebyshev polynomial is substituted into the magnitude response of the normalized Chebyshev lowpass filter along with the ripples attenuation to achieve the ideal response. The transfer function parameters of a fractional‐order filter are optimized using GA to make the magnitude response approximate the ideal response described above. This completes the optimized design of a fractional‐order Chebyshev filter that meets specifications. Given three different sets of design specifications, the fractional‐order Chebyshev filter designed using the proposed method is compared with one designed by another method in the literature. Finally, design examples are presented, stability analysis and Pspice simulations are performed, and an actual circuit is constructed to illustrate the effectiveness of the proposed method.