Survey on Two-Port Network-Based Fractional-Order Oscillators

This chapter merges the fractional calculus and two-port networks in oscillator design. The fractional-order elements ? and ? add extra degrees of freedom that increase the design flexibility and frequency band while providing control over the phase difference. A prototype of the fractional-order two-port network oscillators is introduced. It consists of a general two-port network and three impedances distributed as input, output, and a feedback impedance. Three different two-port network classifications are obtained according to the ground location. This chapter focuses on one of these classifications from which two derived prototypes can be extracted. The general analytical formulas of the oscillation frequency and condition as well as the phase difference are derived in terms of the transmission matrix parameter of a general two-port network. Different active building blocks are used to serve as a two-port network. Numerical, Spice simulations, and experimental results are given to validate the presented analysis. © 2018 Elsevier Inc. All rights reserved.

A survey on memristor active emulation circuits in the fractional-order domain

Chua postulated a new element called a memristor, contributing flux and charge link. The main characteristic of the memristor is a pinched hysteresis double loop with one pinched point. The memristor’s realization in the fractional-order domain increases the hysteresis loop area’s controllability and frequency range. Besides, the fractional-higher-order memristor is realized, achieving more than a pinched point with changes of the pinched point’s location at different values of a. The commercial memristor device is absent until now. For this purpose, scientists concentrated on modeling the memristor achieving its characteristics, and applied it with other circuit elements. This chapter is intended to study the previously proposed memristor emulator in a fractional-order domain dependent on commercial active building blocks. The memristance emulation circuits are classified into four categories: circuits based on operational amplifiers, second-generation current conveyor family circuits, current-feedback operational amplifiers, and complementary metal-oxide semiconductors. The introduced circuits are compared, also the PSPICE, and experimental results confirm the selected circuits. © 2022 Elsevier Inc. All rights reserved.