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.
Fractional Order Sallen–Key and KHN Filters: Stability and Poles Allocation
This paper presents the analysis for allocating the system poles and hence controlling the system stability for KHN and Sallen–Key fractional order filters. The stability analysis and stability contours for two different fractional order transfer functions with two different fractional order elements are presented. The effect of the transfer function parameters on the singularities of the system is demonstrated where the number of poles becomes dependent on the transfer function parameters as well as the fractional orders. Numerical, circuit simulation, and experimental work are used in the design to test the proposed stability contours. © 2014, Springer Science+Business Media New York.
Introduction
This chapter summarizes the basic linear circuit elements (resistor, capacitor, inductor, and fractional-order elements) with their basic fundamentals and characteristic graphs. Each element was defined by a relation between the state variables of the network: current I, voltage V, charge Q, and flux ?. It also investigates the basic fundamentals of the memristor, its historical background, and its advantages over the last few decades. Moreover, the organization of the book is also discussed. © 2015, Springer International Publishing Switzerland.
Memristor based N-bits redundant binary adder
This paper introduces a memristor based N-bits redundant binary adder architecture for canonic signed digit code CSDC as a step towards memristor based multilevel ALU
Neuron model with simplified memristive ionic channels
A simplified neuron model is introduced to mimic the action potential generated by the famous Hodgkin-Huxley equations by using the genetic optimization algorithm
Design of Positive, Negative, and Alternating Sign Generalized Logistic Maps
The discrete logistic map is one of the most famous discrete chaotic maps which has widely spread applications
Encryption applications of a generalized chaotic map
This paper presents the mathematical aspects of a generalized Sine map with arbitrary powers and scaling factor
Power dissipation of memristor-based relaxation oscillators
Recently, many reactance-less memristive relaxation oscillators were introduced, where the charging and discharging processes depend on memristors
Pinched hysteresis with inverse-memristor frequency characteristics in some nonlinear circuit elements
Abstract Pinched hysteresis is considered to be a signature of the existence of memristance