Abstract
Fractional-order circuits and systems incorporate fractional calculus concepts and have immense potential in the fields of signal processing, control systems, biomedical instrumentation, and many more. In general, the dynamic system behavior can be modeled more accurately using fractional-order systems (FOSs) than their integer-order counterparts. Further, the system accuracy increases with increasing the order of the FOS. Fractional-order circuits are an example of FOS, which can be designed using fractional-order elements (FOEs) with lower fractional order (0<α<1) or higher-order FOEs (α>1, where α is a compound value). The higher-order FOEs may be realized using inverted impedance multiplier circuit (IIMC)-, generalized impedance converter (GIC)-, or functional block diagram-based approaches. This chapter is devoted to the detailed description of various realization methods of higher-order FOEs, and a brief background of the lower-order FOEs realization is also included for the sake of continuity. Various design methods have been illustrated using an active block operational transconductance amplifier. A parallel resonator block (PRB)-based higher-order current mode fractional-order filter designed using higher-order FOEs is also presented as an application.
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