Fractal Elements and their Applications

This book describes a new type of passive electronic components, called fractal elements, from a theoretical and practical point of view. The authors discuss in detail the physical implementation and design of fractal devices for application in fractional-order signal processing and systems. The concepts of fractals and fractal signals are explained, as well as the fundamentals of fractional calculus. Several implementations of fractional impedances are discussed, along with comparison of their performance characteristics. Details of design, schematics, fundamental techniques and implementation of RC-based fractal elements are provided.

Presents new passive electronic components, in which the relationship between the current and the voltage at the terminals is described by differential equations of fractional order (i.e., fractal impedance elements or "fractal elements") Emphasizes the theoretical understanding, hardware implementation and practical application of fractional-order dynamics Enables engineers with the tools of fractal geometry and fractional analysis to develop new instruments, devices and systems for signal processing Includes supplementary material: sn.pub/extras

Autorentext

Anis Kharisovich Gil'mutdinov is a Professor at Kazan National Research Technical University, in Kazan, Russia.

Pyotr Arkhipovich Shakos is a Professor at Kalashnikov State Technical University in Izhevsk, Russia.

Reyad El-Khazali is an Associate Professor of Electronics Engineering at Khalifa University of Science, Technology, and Research.

Inhalt

1 Fractals and modelling of fractal Elements and processes.- 2 Fractal calculus fundamentals.- 3 Fractal elements.- 4 Design and Implementation of Thin RC-EDP Films.- 5 Schematic Realization of RC-EDP Circuits.- 6 Design and Fabrication of RC-EDP circuits.- 7 Nonlinear Structure of RC-EDP Circuits.- 8 Applications of fractal elements.- 9 Modeling of RC-EDP Circuits.- 10 Calculation one-dimensional RC-EDP primary parameters.- 11 Numerical methods of R-C-0-EDP Fractal Elements.- 12 Primary parameters calculation of the RC-EDP using generalized RCG-EDP devices.