A.A. Arbuzov, R.R. Nigmatullin

Self-similar electric circuits, which allow simulating real processes (dielectric relaxation phenomena [1, 2], electrolyte processes [3, 4, 11] and others) have been considered. Exact functional equations for self-similar electric circuits admittance Y(jω) connecting in series or parallel have been found and solved. Based on self-similar structure of electric circuit it has been shown that in frequency domain the admittance consists of the sum of power-law expressions with one real and a pair of the complex conjugated power-law exponents. Thus, it has been shown that a set of micromotions taking place in different subcircuits and connecting the charge transfer (the capacity C) or elementary resistance of the medium (the ohmic resistance R) reduces to the power-law dependence of the type (jωτ)ν. It has been shown also that the values of the power-law exponents do not depend on (if the number of chain elements is becoming large) the concrete form of the elementary cell of the RC-circuit. It was also possible to define these power-law exponents as a dynamic fractal dimension (see (2.24)) and so give them a new geometrical/physical meaning and extended interpretation.