Simulation of fractal immittance by analog circuits: An approach to the optimized circuits

Fractal immittance, expressed by an admittance s(a) (0 < \a\ < 1), is simul ated by the analog circuits composed of finite numbers of conventional elem ents, resistance R, capacitance C and inductance L, based on the distribute d-relaxation-time models. The correlation between the number of R-C or R-L pairs and the optimum pole interval to give the widest bandwidth is estimat ed for each a-value by the numerical calculation for each circuit against a given criterion with respect to the phase angle. It is found that the band width of 5 decades with a phase-angle error of +/-1 degrees can be composed for \a\ = 0.1-0.9 using eighteen pairs or less of the elements.