M. R. Vyaselev, A. V. Tribunskih, M. V. Petrovskaya, V. V. Petrovskii

In order to develop devices that electrically realize a real-time fractal operators of arbitrary order in complex system signal simulation and processing, the method of automatic optimal synthesis of fractal multilink RC-dipoles was proposed, developed and investigated. They have required transformation characteristics with specified fractional exponent in generalized frequency slot with given accuracy with minimum number of links. The synthesis is based on minimization the differences of exact frequency dependence of real and ideal dipole impedance. In order to verify the accuracy of the algorithm and synthesis program according to its results which were obtained with different input data (fractional exponent, frequency slot and precision), dimensional values of particular dipole scheme parameters of 1, 2 and 3 decade frequency range were defined. This scheme implementation using Multisim and further acquisition of their amplitude and phase frequency characteristics confirmed the accuracy of synthesis results. The properties of fractal dipoles obtained by this synthesis were investigated in order to: - assess its frequency characteristics sensitivity to deviation of link values from its synthetic values; - determine the link number dependence of frequency slot; - identify maximal attainable frequency range depending on fractional exponent; - compare synthesis results performed on both frequency dependencies (amplitude and phase frequency characteristics) and only on phase frequency characteristics; - determine the laws of heterogeneity of fractal links depending on desired fractional exponent and frequency range. It was concluded that the above synthesis method allows to reveal optimal law of heterogeneity not only for discrete, but also for continuum dispersed fractal RC-structure with desired properties.