Frequency behavior of self-similar ladder circuits

The fractal immittance, Y(ω)∝ωa or Z(ω)∝ω−a (0<a<1) with an optional a-value, has been found to be simulated using self-similar ladder circuits with each set of elements, R or C, forming a geometric progression. The optimum bandwidth Bop is numerically calculated for a given criterion with respect to the phase angle as a function of the number of rungs n involved in the ladder. Bop≥5 with a phase-angle error of ±1/2° is found to be attainable for a=0.25–0.75 by 18 rungs or less, indicating the availability of the self-similar ladders for the hardware realization of fractal immittance.