Experimental studies on realization of fractional inductors and fractional‐order bandpass filters

Abstract

Summary This paper presents the hardware realization and performance study of fractional inductors of order 0 < α < 2. The fractional inductors used in this work have been realized with the help of general impedance converter circuit and fractional capacitors. Impedance characterization of fractional inductors with different exponents has been carried out experimentally. Also a generalized approach to design a fractional‐order bandpass filter is discussed in this work. The fractional‐order bandpass filter consists of a series combination of a resistor, a fractional inductor of order 1 < α < 2, and a fractional capacitor of order 0 < β < 1. The performance of fractional‐order bandpass filters has been studied and compared with corresponding integer‐order filters through both experimentation and simulation. Copyright © 2014 John Wiley & Sons, Ltd.

Comparative Study of Discrete Component Realizations of Fractional-Order Capacitor and Inductor Active Emulators

“…The behavior of fractional-order inductors is approximated through the combination of a fractional-order capacitor emulator and a Generalized Impedance Converter (GIC). 23,6 Another solution, offering more design°exibility than that o®ered by the previous one, is the employment of fractional-order integrator/di®erentiation stage and, also, an appropriate voltage-to-current (V =I) converter. 24,25 The fractional-order integrator/di®er-entiator is approximated by an appropriate integer-order transfer function and the achieved accuracy depends on the order of approximation which re°ects into the circuit complexity required for implementing the corresponding transfer function.…”

“…Owing to the interdisciplinary nature of the fractional calculus, 1 there is a growing research interest in the development of fractional-order circuits including¯lters, [2][3][4][5][6][7][8][9] oscillators, [10][11][12][13] biological tissues emulators, 14 and energy storage devices. 15 In these applications, the basic building blocks are the fractional-order capacitors and/or fractional-order inductors.…”

Digitally programmed fractional-order Chebyshev filters realizations using current-mirrors

“…It should be mentioned at this point that this CDN is also constructed from currentmirrors and this provides modularity to the whole system. (11) where b j is the j-th digital bit.…”

Electronically Tunable Fully Integrated Fractional-Order Resonator

“…Test results of a chip containing fabricated CMOS fractional-order capacitor emulators were recently reported in [10]. To-date, realization of a fractional-order inductor has only been approached through the realization of a fractionalorder capacitor using appropriately configured RC networks [11] and then through the employment of a Generalized Impedance Converter (GIC) to transform it into an inductor [12], [13], [14], [15], [16] or using discrete Current Feedback Operational Amplifiers (CFOAs) as active elements [17].…”