Design and Realization of Fractional Systems for Signal Processing Applications

The concept of fractional calculus has emerged as one of the most effective mathematical tools for improving the performance of electrical circuits and systems. By using this tool electronic filters, oscillators, integrators, differentiators, and several other signal processing circuits and systems are realized in fractional sense. Consequently, these systems are known as fractional-order systems, and they enjoy more degree of freedom. Fractional-order systems also have higher accuracy and flexibility than the conventional systems. The fractional-order systems utilize fractance devices (FDs) in place of conventional passive circuit components. Although these FDs are not available commercially as a lumped element; they can be approximated using a semi-infinite R-C/R-L tree or ladder network. These R-C/R-L networks based FDs degrade the performance of the overall system in terms of power efficiency, noise, circuit complexity, and cost, etc. In this work, an attempt has been made to develop and realize efficient designs of fractional-order circuits and systems for various signal processing applications. Initially, fractional-order low pass filters have been designed and realized using modern current mode active building blocks (ABBs) as an active device. Since, the modern ABBs have higher linearity and dynamic range, more power efficiency, wider bandwidth, and large arithmetic operational capabilities; fractional-order filters realized using these ABBs show improved performance over the existing designs. Further, a compact fractional-order multiphase oscillator has been realized using DVCC (Differential voltage current conveyor) as an active block. This multiphase fractional oscillator provides independent control on the phase and the frequency of the oscillatory waveforms. In addition to this, a novel approach has also been presented to miniaturize the physical structure of fractional-order oscillators by replacing the conventional R-C/R-L tree or ladder network based FDs with an efficient R-C/R-L pair based FDs. The ii proposed R-C/R-L pair based FDs require only two passive components to approximate an FD. Hence, proposed FDs not only miniaturize the overall circuit but also improve the efficiency, noise performance, and reduce the cost of the fractional-order system. Finally, a multipurpose electrical system has been designed by cascading logarithmic amplifier with a fractional-order differentiator that can be used in various analog signal (ASP) processing applications.