Analysis and realization of a switched fractional‐order‐capacitor integrator

Abstract

Using fractional calculus, we analyze a classical switched-capacitor integrator when a fractional-order capacitor is employed in the feed-forward path. We show that using of a fractional-order capacitor, significantly large time constants can be realized with capacitances in the feedback path much smaller in value when compared with a conventional switched-capacitor integrator. Simulations and experimental results using a commercial super-capacitor with fractional-order characteristics confirmed via impedance spectroscopy are provided.

All‐Solid‐State Double‐Layer Capacitors Using Binderless Reduced Graphene Oxide Thin Films Prepared by Bipolar Electrochemistry

“…The plots are tilted from vertical and thus cannot be modeled using a simple circuit . We used non‐linear least squares fitting to an equivalent circuit comprised of a series resistance ( ) with a parallel association of constant phase element (CPE) ( in which the pseudocapacitance is in units of F s , and can take on values between 1, for an element acting as an ideal capacitor, to 0, for a resistor) and a parallel resistance (see inset in Figure (a)), such that: …”

“…In Figure 4 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 The plots are tilted from vertical and thus cannot be modeled using a simple R s C circuit. [4,5,[18][19][20][21] We used non-linear least squares fitting to an equivalent circuit comprised of a series resistance (R s ) with a parallel association of constant phase element (CPE) (Z CPE ¼ 1=ðjwÞ a Q in which the pseudocapacitance Q is in units of F s aÀ1 , and a can take on values between 1, for an element acting as an ideal capacitor, to 0, for a resistor) and a parallel resistance R p (see inset in Figure 4(a)), such that:…”

“…As a result, tremendous progress have been achieved in (i) fabricating these device through the use of different electric double-layer carbon-based materials [1][2][3][6][7][8][9][10] and pseudocapacitive materials, [11][12][13][14][15][16] (ii) the use of different inexpensive fabrication methods such as screen-printing, [9] spray-coating, [8,17] and inkjet print-ing, [7] and also through (iii) the development of new time-and frequency-domain modeling tools to evaluate their metrics and energy storage performance. [4,5,[18][19][20][21][22] Nonetheless, with the continuous quest for miniaturization of portable electronics, new micro-fabrication techniques of thin film EDLCs are needed. This is because the traditional nanopowder-based energy devices scale down poorly in size and are not well-suited for the volume restrictions of small electronics.…”

Comparative analysis to determine the accuracy of fractional derivatives in modeling supercapacitors

“…The basic equivalent circuit for modeling a supercapacitor is an equivalent resistance in series ( R s ) and an ideal capacitor C , as discussed in Spyker and Nelms and Psychalinos et al A more interesting model for engineering analysis is observed in Figure , which contains the same equivalent resistance in series R s and the capacitor C but includes an equivalent resistance in parallel R p with the capacitor. The resistance R p serves to take into account the effect of the capacitor leakage current .…”

Electrical circuits RC, LC, and RL described by Atangana–Baleanu fractional derivatives

“…Fractional calculus (FC) is a generalization of ordinary calculus; the FC allows investigating the nonlocal response of different phenomena. Different works concerning to the electrical components modeling and related to the behavior of the circuits and systems with memristors, meminductors, or memcapacitors have been reported in [1][2][3][4][5][6][7][8][9][10]. According to the authors in [11][12][13][14][15][16][17], the aforementioned elements have a non-conservative feature that involves irreversible dissipative effects such as ohmic friction or thermal memory due to the effects of the electric and magnetic fields.…”