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.
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.
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.
RF MEMS fractal capacitors with high self-resonant frequencies
This letter demonstrates RF microelectromechanical systems (MEMS) fractal capacitors possessing the highest reported self-resonant frequencies (SRFs) in PolyMUMPS to date
Low-voltage puzzle-like fractal microelectromechanial system variable capacitor suppressing pull-in
This Letter introduces an electrostatically actuated fractal MEMS variable capacitor that, by utilising the substrate, extends the tuning range (TR) beyond the theoretical limit of 1
The fractional-order modeling and synchronization of electrically coupled neuron systems
In this paper, we generalize the integer-order cable model of the neuron system into the fractional-order domain, where the long memory dependence of the fractional derivative can be a better fit for the neuron response
An expression for the voltage response of a current-excited fractance device based on fractional-order trigonometric identities
We report a closed-form expression of the voltage response of a current-excited fractance device
Controllable V-shape multiscroll butterfly attractor: System and circuit implementation
In this paper, a new controllable V-shape multiscroll attractor is presented, where a variety of symmetrical and unsymmetrical attractors with a variable number of scrolls can be controlled using new staircase nonlinear function and the parameters of the system