Gil’mutdinov A.K., Ushakov P.A., El-Khazali R. Fractal Elements and their Applications

Springer, 2017. — XVIII, 252 p. — (Analog Circuits and Signal Processing). — ISBN: 978-3-319-45248-7.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.Modeling of Fractal Elements and Processes.
Concept of Fractals, Self-Similarity, and Scaling.
Dimension Types.
Regular Fractals.
Irregular Random Fractals.
Multifractals.
Fractal Signals.
Physical Meaning of Hurst Parameter.
Relation Between Fractality and Spectrum Response.
Examples of Signal Analysis.Fractal Calculus Fundamentals.
Preliminaries.
Properties of Fractional-Order Integrals and Derivatives.
Laplace Transform of Fractional-Order Operators.
Fourier Transform of Fractional-Order Operators.
Dynamics of Fractional-Order Transfer Functions.
Fractional-Order Electrical and Electronic Systems.Fractal Elements.
Fractal Impedances and Fractal Element.
Implementation of Fractal Impedances Using Electrochemical Converters.
Implementation of Fractal Impedances (Immittances) Using RC Circuits with Lumped Parameters.
Realization of Fractal Impedances Using RC Circuits with Distributed Parameters.
Fabrication of Fractal Impedances Using Nanostructured Materials.
Comparison of Fractal Element Characteristics Using Different Fabrication Technology.Design and Implementation of Thin RC-EDP Films.
Classification of Static Heterogeneous Characteristics of RC-EDP Films.
RC-EDP Film Design of Multilayer Structure.
Design Development of RC-EDP Films by Changing Layers Geometry.
Design Development of RC-EDP Film Using Layers Overlapping.
Design Development of RC-EDP Films via Contacts Combination.
Design Development of RC-EDP Films via Layers Cutouts.Schematic Realization of RC-EDP Circuits.
Preliminaries and Background.
Characteristics of One-Dimensional (OD) Homogeneous and Heterogeneous R-C-0 EDP Structure.
Connection Circuits of OD R-C-NR-Structured EDP Circuits.
Connection of an 0-C-R-NC-0-Structured EDP Circuits.
Effect of Number of RС-EDP Terminals on Circuits Connections.
Compound Structure of RС-EDP Circuits.Design and Fabrication of RC-EDP Circuits.
Preliminaries and Background.
Thin-Film RC-EDP Fabrication Methods.
Performance Analysis and Parameter Tuning of RC-EDP Circuits.Nonlinear Structure of RC-EDP Circuits.
Presuppositions.
External Field Effect on the Fabrication of RC-EDP Resistive Parameters.
External Field Effect on the Fabrication of RC-EDP Dielectric Layer Materials.
Nonlinear RC-EDP Circuits.Applications of Fractal Elements.
Application of Fractal Elements and Devices in Signal Processing.
Application of the RC-EDP to Model Fractal Processes and Objects.
Application of RC-EDP Devices in Fractional-Order Dynamics and Control.
Promising Application Areas of the RC-EDP Devices.
The Universal Simulation Environment with Distributed RLCG Parameter Method.Modeling of RC-EDP Circuits.
General Model of R1-C1-R2-C2-R3-Layered RC-EDP Devices.
Classification of R1-C-R2-Layered RC-EDP Based on Potential Distribution in Resistive Layers.Calculation of One-Dimensional RC-EDP Primary Parameters.
Preliminaries.
Y-Parameter Calculation of ODHom R-С-0-Layered EDP Devices.
Y-Parameter Calculation of ODHet R-С-0-Layered EDP Devices.
Y-Parameter Calculation of ODHom R1-G1-C1-R-C2-G2-R2-Layered EDP Devices.Numerical Methods of R-C-0-EDP Fractal Elements.
Preliminaries.
Finite Distributed Element Method.
Application of Finite Distributed Element Method to Calculate the ODHet RC-EDP Primary Parameters.
Application of Finite Distributed Element Method to Calculate the TDHom RС-EDP Y-Parameters.Primary Parameter Calculation of the RC-EDP Using Generalized RCG-EDP Devices.
Generalized Finite Distributed Element Method.
Classification and Synthesis of FDE Using the GFDEM Elements.
Y-Parameter Calculations of One-Dimensional Heterogeneous Structure of RC-EDP Devices Using GFDEM.