A review of the state-of-the-art in fractional-order analog filters

Abstract

Today, there is a great tendency toward using fractional calculus to solve engineering problems. The analog filters are one of the fields in which fractional calculus has attracted significant attention. The invention of the fractance device has led to the possibility of exploring analog filtering techniques from a practical perspective, enlarging the horizon to a wider frequency range, with increased robustness to component variation, stability and noise reduction. In addition to the use of fractance device, fractional-order analog filters (FOAFs) can also be realized by integer-order approximation of the $s^{\alpha }$, optimization and curve fitting techniques (power-law/double-order) methods. The design of FOAFs is thoroughly studied and presented in a manifold of research works, mostly from a theoretic perspective. Most of these papers present the physical realization of the proposed FOAF from a conceptual perspective. This survey paper gives an account of the progress made on the evolution of FOAFs so far and highlights several unresolved problems and issues, including the lack of standardization in design methods, challenges in realizing fractional operators in hardware, complications related to parameter sensitivity and tuning, computational complexity and efficiency, stability analysis and robustness, difficulties in integrating with emerging technologies, and scalability challenges. Furthermore, the supremacies of having a near-ideal FO behavior in filter application are stated and the significant advantages of FOAFs against integer-order analog filters (IOAFs) are emphasized. The paper, thus, presents the current state-of-the art of FOAFs by providing an appraisal of a variety of realizations of FOAFs.