Systems concept and components of fractal radio electronics: Part I. Development stages and the state of the art

A systemization is performed for the results of theoretical and experimental investigations that were obtained in radio physics and radio engineering with the help of fractal theory and the mathematical theory of fractional dimension and fractional operators with consideration for the scaling effects of real radio signals and electromagnetic fields. Classification and the analysis and synthesis methods of the components of fractal radio electronics (resistive-capacitive components with distributed parameters) with prescribed frequency characteristics, as well as the fields of application of such components, are considered. It is shown that non-linear, parametric, and other properties of simulated objects can be considered with the use of vectors of electrophysical parameters of layers and design parameters. New promising design versions of components with fractal dimensions, namely, fractal impedances, which can be used in various devices of fractal radio electronics, are proposed.

[1]  B. Gnedenko,et al.  Limit Distributions for Sums of Independent Random Variables , 1955 .

[2]  S. Gubin,et al.  Electrical and magnetic properties of nanomaterials containing iron or cobalt nanoparticles , 2007 .

[3]  Igor M. Sokolov,et al.  Physics of Fractal Operators , 2003 .

[4]  Jean-Philippe Bouchaud,et al.  Lévy Statistics and Laser Cooling , 2001 .

[5]  Luciano Pietronero,et al.  FRACTALS IN PHYSICS , 1990 .

[6]  William Feller,et al.  An Introduction to Probability Theory and Its Applications , 1967 .

[7]  W. E. Heinlein,et al.  Active Filters for Integrated Circuits: Fundamentals and Design Methods , 1974 .

[8]  Raoul R. Nigmatullin,et al.  Fractional integral and its physical interpretation , 1992 .

[9]  Y. Kim,et al.  The fractal random array , 1986, Proceedings of the IEEE.

[10]  Mohammed Ghausi,et al.  Introduction to distributed-parameter networks , 1968 .

[11]  P. S. Castro.  Microsystem circuit analysis , 1961, Electrical Engineering.

[12]  A. Méhauté,et al.  Semiconductor-metal transition upon intercalation in LixZrSe2 , 1981 .

[13]  I. Podlubny,et al.  Analogue Realizations of Fractional-Order Controllers , 2002 .

[14]  G. Ablart,et al.  Microwave characterization and modeling of the surface impedance of fractal structure copper films , 1998 .

[15]  Benoit B. Mandelbrot,et al.  Fractal Geometry of Nature , 1984 .

[16]  Karabi Biswas,et al.  Realization of a Constant Phase Element and Its Performance Study in a Differentiator Circuit , 2006, IEEE Transactions on Circuits and Systems II: Express Briefs.

[17]  Jordi Romeu,et al.  On the behavior of the Sierpinski multiband fractal antenna , 1998 .

[18]  Dwight L. Jaggard,et al.  On Fractal Electrodynamics , 1990 .

[19]  I. P. Gerasimov.  Collection of Articles , 1967 .

[20]  S. Roy.  On the Realization of a Constant-Argument Immittance or Fractional Operator , 1967, IEEE Transactions on Circuit Theory.

[21]  S. D. Roy.  Constant argument immittance realization by a distributed RC network , 1974 .

[22]  K. Heizer,et al.  Distributed Rc Networks With Rational Transfer Functions , 1962 .

[23]  R. G. Laha.  Review: V. M. Zolotarev, One-dimensional stable distributions , 1989 .

[24]  D. Stoyan,et al.  Mandelbrot, B. B., Fractals: Form, Chance, and Dimension. San Francisco. W. H. Freeman and Company. 1977. 352 S., 68 Abb., $14.95 , 1979 .

[25]  A. R. Analouei,et al.  The Pole-Zero Locations of Trimmed Distributed RC Active Notch Filters , 1984 .

[26]  Andrzej Guziński.  An active filter with a distributed RGC line , 1976 .

[27]  V. Zolotarev.  One-dimensional stable distributions , 1986 .

[28]  N. G. Burrow,et al.  The Dominant Poles of Trimmed Uniform Distributed RC Networks Obtained from Their Transient Response , 1982 .

[29]  R. M. Crownover,et al.  Introduction to fractals and chaos , 1995 .

[30]  R. Lerner,et al.  The Design of a Constant-Angle or Power-Law Magnitude Impedance , 1963 .

[31]  R. Morrison,et al.  RC Constant-Argument Driving-Point Admittances , 1959 .

[32]  D. Almond,et al.  Modelling the 'universal' dielectric response in heterogeneous materials using microstructural electrical networks , 2006 .

[33]  Jordi Romeu Robert,et al.  An iterative model for fractal antennas: application to the Sierpinski gasket antenna , 2000 .

[34]  P. Levy.  Théorie de l'addition des variables aléatoires , 1955 .

[35]  D. Tanaka,et al.  Two-dimensional analysis of Bessel RC lines , 1971 .