Recently, the memristor based relaxation oscillators become an important topic in circuit theory where the reactive elements are replaced by memristor which occupies a very small area
Review of the missing mechanical element: Memdamper
In this paper, the analogy between electrical and mechanical quantities is reviewed
Comparative study of fractional filters for Alzheimer disease detection on MRI images
This paper presents a comparative study of four fractional order filters used for edge detection
Generalized chaotic maps and elementary functions between analysis and implementation
Nonlinear analysis and chaos have many applications in communications, cryptography, and many other fields
Memristor-based data converter circuits
This paper introduces data converter circuit based on memristors
A fractional-order dynamic PV model
A dynamic model of Photo-Voltaic (PV) solar module is important when it is utilized in conjunction with switching circuits and in grid connected applications
Fractional-order synchronization of two neurons using Fitzhugh-Nagumo neuron model
This paper studies the synchronization of two coupled neurons using Fitzhugh-Nagumo model in the fractional-order domain
Fractional-order oscillators
Fractional-order calculus is the branch of mathematics which deals with non-integerorder differentiation and integration. Fractional calculus has recently found its way to engineering applications; particularly electronic circuits with promising results showing the feasibility of fabricating fractional-order capacitors on silicon. Fractionalorder capacitors are lossy non-deal capacitors with an impedance given by Zc = (1/j?C)?, where C is the pseudo-capacitance and ? is its order (0 < ? ? 1). When these fractional-order capacitors are employed within an oscillator (sinusoidal or relaxation) circuit, this oscillator is called a fractional-order oscillator and is described by non-integer-order differential equations. Therefore, an oscillator of order 1.5 or 2.6 is possible to obtain. While the oscillation frequency in integer-order oscillators is related to their RC time constants, fractional-order oscillators have their oscillation frequencies also related to ?. This adds more design freedom and enables extremely high or extremely low oscillation frequencies even with large RC time constants. This chapter aims at reviewing the theory of designing fractional-order oscillators accompanied by several design examples. Experimental results are also shown. © The Institution of Engineering and Technology 2017. All rights reserved.
Fractional Order Oscillator Design Based on Two-Port Network
In this paper, a general analysis of the generation for all possible fractional order oscillators based on two-port network is presented. Three different two-port network classifications are used with three external single impedances, where two are fractional order capacitors and a resistor. Three possible impedance combinations for each classification are investigated, which give nine possible oscillators. The characteristic equation, oscillation frequency and condition for each presented topology are derived in terms of the transmission matrix elements and the fractional order parameters ? and ?. Mapping between some cases is also illustrated based on similarity in the characteristic equation. The use of fractional order elements ? and ? adds extra degrees of freedom, which increases the design flexibility and frequency band, and provides extra constraints on the phase difference. Study of four different active elements, such as voltage-controlled current source, gyrator, op-amp-based network, and second-generation current-conveyor-based network, serve as a two-port network is presented. The general analytical formulas of the oscillation frequency and condition as well as the phase difference between the two oscillatory outputs are derived and summarized in tables for each designed oscillator network. A comparison between fractional order oscillators with their integer order counterparts is also illustrated where some designs cannot work in the integer case. Numerical Spice simulations and experimental results are given to validate the presented analysis. © 2015, Springer Science+Business Media New York.
Fractional-order mutual inductance: Analysis and design
This paper introduces for the first time the generalized concept of the mutual inductance in the fractional-order domain where the symmetrical and unsymmetrical behaviors of the fractional-order mutual inductance are studied. To use the fractional mutual inductance in circuit design and simulation, an equivalent circuit is presented with its different conditions of operation. Also, simulations for the impedance matrix parameters of the fractional mutual inductance equivalent circuit using Advanced Design System and MATLAB are illustrated. The Advanced Design System and MATLAB simulations of the double-tuned filter based on the fractional mutual inductance are discussed. A great matching between the numerical analysis and the circuit simulation appears, which confirms the reliability of the concept of the fractional mutual inductance. Also, the analysis of the impedance matching using the fractional-order mutual inductance is introduced. © 2015 John Wiley & Sons, Ltd.