Traditional continuous-time filters are of integer order. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations in which case integer-order filters are only a tight subset of fractional-order filters. In this work, we show that low-pass, high-pass, band-pass, and all-pass filters can be realized with circuits incorporating a single fractance device. We derive expressions for the pole frequencies, the quality factor, the right-phase frequencies, and the half-power frequencies. Examples of fractional passive filters supported by numerical and PSpice simulations are given. © 2008 World Scientific Publishing Company.
Memcapacitor response under step and sinusoidal voltage excitations
Recently, mem-elements have become fundamental in the circuit theory through promising potential applications based on the built-in memory-properties of these elements. In this paper, the mathematical analysis of the memcapacitor model is derived and the effect of different voltage excitation signals is studied for the linear dopant model. General closed form expressions and analyses are presented to describe the memcapacitor behavior under DC step and sinusoidal voltage excitations. Furthermore, the step and sinusoidal responses are used to analyze the memcapacitor response under any periodic signal using Fourier series expansion where the effect of the DC component on the output response is investigated. In addition, the stored energy in the memcapacitor under step, sinusoidal and square wave excitations is discussed. Moreover, the analysis of series and parallel connection of N non-matched memcapacitors in general is introduced and special cases of matched memcapacitors are discussed. The derived equations are verified using SPICE simulations showing great matching. © 2014 Elsevier Ltd. All rights reserved.
Optimal Charging and Discharging of Supercapacitors
In this paper, we discuss the optimal charging and discharging of supercapacitors to maximize the delivered energy by deploying the fractional and multivariate calculus of variations. We prove mathematically that the constant current is the optimal charging and discharging method under R s -CPE model of supercapacitors. The charging and round-trip efficiencies have been mathematically analyzed for constant current charging and discharging. © 2020 The Electrochemical Society (“ECS”). Published on behalf of ECS by IOP Publishing Limited.
Resistive-less memcapacitor-based relaxation oscillator
Recently, the realization of the conventional relaxation oscillators was introduced based on memristors. This paper validates the concept using two series memcapacitors in general which is applicable for a capacitor and memcapacitor as well. Furthermore, the necessary conditions for oscillation are introduced, and a generalized closed-form expression for the oscillation frequency is derived. Two special cases are introduced and verified using PSPICE simulations showing a perfect matching. Copyright © 2014 John Wiley & Sons, Ltd.
Boundary Dynamics of Memcapacitor in Voltage-Excited Circuits and Relaxation Oscillators
This paper discusses the boundary dynamics of the charge-controlled memcapacitor for Joglekar’s window function that describes the nonlinearities of the memcapacitor’s boundaries. A closed form solution for the memcapacitance is introduced for general doping factor (Formula presented.)p. The derived formulas are used to predict the behavior of the memcapacitor under different voltage excitation sources showing a great matching with the circuit simulations. The effect of the doping factor (Formula presented.) on the time domain response of the memcapacitor has been studied as compared to the linear model using the proposed formulas. Moreover, the generalized fundamentals such as the saturation time of the memcapacitor are introduced, which play an important role in many control applications. Then the boundary dynamics under sinusoidal excitation are used as a basis to analyze any periodic signal by Fourier series, and the results have been verified using PSPICE simulations showing a great matching. As an application, two configuration of resistive-less memcapacitor-based relaxation oscillators are proposed and closed form expressions for oscillation frequency and conditions for oscillation are derived in presence of nonlinear model. The proposed oscillator is verified using PSPICE simulation showing a perfect matching. © 2015, Springer Science+Business Media New York.
Simple floating voltage-controlled memductor emulator for analog applications
The topic of memristive circuits is a novel topic in circuit theory that has become of great importance due to its unique behavior which is useful in different applications. But since there is a lack of memristor samples, a memristor emulator is used instead of a solid state memristor. In this paper, a new simple floating voltage-controlled memductor emulator is introduced which is implemented using commercial off the shelf (COTS) realization. The mathematical modeling of the proposed circuit is derived to match the theoretical model. The proposed circuit is tested experimentally using different excitation signals such as sinusoidal, square, and triangular waves showing an excellent matching with previously reported simulations.
Memristor-based voltage-controlled relaxation oscillators
This paper introduces two voltage-controlled memristor-based reactance-less oscillators with analytical and circuit simulations. Two different topologies which are R-M and M-R are discussed as a function of the reference voltage where the generalized formulas of the oscillation frequency and conditions for oscillation for each topology are derived. The effect of the reference voltage on the circuit performance is studied and validated through different examples using PSpice simulations. A memristor-based voltage-controlled oscillator (VCO) is introduced as an application for the proposed circuits which is nano-size and more efficient compared to the conventional VCOs. Copyright © 2013 John Wiley & Sons, Ltd.
Meminductor response under periodic current excitations
Recently, the mem-elements-based circuits have been addressed frequently in the nonlinear circuit theory due to their unique behavior. Thus, the modeling and characterizing of the mem-elements has become essential, especially studying their response under any excitation signal. This paper investigates the response of the meminductor under DC, sinusoidal, and periodic current signals for the first time. Furthermore, a meminductor emulator is developed to fit the obtained formulas which are built using commercial off the shelf components. The proposed analysis offers closed form expressions for the meminductance for each case. Moreover, many fundamentals and properties are derived to understand the responses such as the maximum saturation time in case of the DC response. A general closed form expression for the meminductance is derived under any periodic waveform, and this formula has been validated by applying a square wave as an example. © 2013 Springer Science+Business Media New York.
Non linear dynamics of memristor based 3rd order oscillatory system
In this paper, we report for the first time the nonlinear dynamics of three memristor based phase shift oscillators, and consider them as a plausible solution for the realization of parametric oscillation as an autonomous linear time variant system. Sustained oscillation is reported through oscillating resistance while time dependent poles are present. The memristor based phase shift oscillator is explored further by varying the parameters so as to present the resistance of the memristor as a time varying parameter, thus potentially eliminating the need of external periodic forces in order for it to oscillate. Multi memristors, used simultaneously with similar and different parameters, are investigated in this paper. Mathematical formulas for analyzing such oscillators are verified with simulation results and are found to be in good agreement. © 2011 Elsevier Ltd. All rights reserved.
Charge controlled memristor-less memcapacitor emulator
Recently, many promising applications are oriented towards the new memristive elements. But since these elements are not commercially available yet, the memristive elements emulators are very important. Introduced is a new memcapacitor emulator without using any memristor. The circuit concept and mathematical modelling are discussed analytically and numerically to validate the operation of the proposed emulator. Moreover, the proposed emulator is assembled using commercial off-the-shelf components and verified using PSpice simulations. © 2012 The Institution of Engineering and Technology.