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.
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.
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.
First-order filters generalized to the fractional domain
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.
On the generalization of second-order filters to the fractional-order domain
This work is aimed at generalizing the design of continuous-time second-order filters to the non-integer-order (fractional-order) domain. In particular, we consider here the case where a filter is constructed using two fractional-order capacitors both of the same order ?. A fractional-order capacitor is one whose impedance is Zc = 1/C(j?) ?, C is the capacitance and ? (0 < ? ? 1) is its order. We generalize the design equations for low-pass, high-pass, band-pass, all-pass and notch filters with stability constraints considered. Several practical active filter design examples are then illustrated supported with numerical and PSpice simulations. Further, we show for the first time experimental results using the fractional capacitive probe described in Ref. 1. © 2009 World Scientific Publishing Company.
Fractional-order RC and RL circuits
This paper is a step forward to generalize the fundamentals of the conventional RC and RL circuits in fractional-order sense. The effect of fractional orders is the key factor for extra freedom, more flexibility, and novelty. The conditions for RC and RL circuits to act as pure imaginary impedances are derived, which are unrealizable in the conventional case. In addition, the sensitivity analyses of the magnitude and phase response with respect to all parameters showing the locations of these critical values are discussed. A qualitative revision for the fractional RC and RL circuits in the frequency domain is provided. Numerical and PSpice simulations are included to validate this study. © Springer Science+Business Media, LLC 2012.
Fractional order filter with two fractional elements of dependant orders
This work is aimed at generalizing the design of continuous-time filters in the non-integer-order (fractional-order) domain. In particular, we consider here the case where a filter is constructed using two fractional-order elements of different orders ? and ?. The design equations for the filter are generalized taking into consideration stability constraints. Also, the relations for the critical frequency points like maximum and minimum frequency points, the half power frequency and the right phase frequency are derived. The design technique presented here is related to a fractional order filter with dependent orders ? and ? related by a ratio k. Frequency transformations from the fractional low-pass filter to both fractional high-pass and band-pass filters are discussed. Finally, case studies of KHN active filter design examples are illustrated and supported with numerical and ADS simulations. © 2012 Elsevier Ltd.
Fractional order oscillators based on operational transresistance amplifiers
In this paper, a general analysis of the fractional order operational transresistance amplifiers (OTRA) based oscillator is presented and validated through eight different circuits which represent two classifications according to the number of OTRAs. The general analytical formulas of the oscillation frequency, condition as well as the phase difference are illustrated for each case and summarized in tables. One of the advantages of the fractional-order circuit is the extra degrees of freedom added from the fractional-order parameters. Moreover different special cases {? = ? ? 1, ? ? ? = 1, ? ? ? = 1} are investigated where the conventional case ? = ? = 1 is included in all of them. Also, the effect of the fractional order parameter on the phase difference between the two oscillator outputs is presented which increases the design flexibility and controllability. The effect of the non-ideal characteristics associated with OTRA on the presented oscillator is also studied. A comparison between the fractional order oscillators with their integer order counterpart is also presented to verify the advantages of the added fractional order parameters. Numerical and spice simulations are given to validate the presented analysis. © 2015 Elsevier GmbH.
Hardware realization of a secure and enhanced s-box based speech encryption engine
This paper presents a secure and efficient substitution box (s-box) for speech encryption applications. The proposed s-box data changes every clock cycle to swap the input signal with different data, where it generated based on a new algorithm and a memristor chaotic system. Bifurcation diagrams for all memristor chaotic system parameters are introduced to stand for the chaotic range of each parameter. Moreover, the effect of each component inside the proposed encryption system is studied, and the security of the system is validated through perceptual and statistical tests. The size of the encryption key is 175 bits to meet the global standards for the optimum encryption key width (> 128). MATLAB software is used to calculate entropy, MSE, and correlation coefficient. Both chaotic circuit and encryption/decryption schemes are designed using Verilog HDL and simulated by Xilinx ISE 14.7. Xilinx Virtex 5 FPGA kit is used to realize the proposed algorithm with a throughput 0.536 of Gbit/s. The cryptosystem is tested using two different speech files to examine its efficiency. © 2020, Springer Science+Business Media, LLC, part of Springer Nature.
Generalized model for Memristor-based Wien family oscillators
In this paper, we report the unconventional characteristics of Memristor in Wien oscillators. Generalized mathematical models are developed to analyze four members of the Wien family using Memristors. Sustained oscillation is reported for all types though oscillating resistance and time dependent poles are present. We have also proposed an analytical model to estimate the desired amplitude of oscillation before the oscillation starts. These Memristor-based oscillation results, presented for the first time, are in good agreement with simulation results. © 2011 Elsevier Ltd.