Figure 2 : (a) Single stage RC tree. (b) Equivalent RC tree for fractional order capacitor of any order [8, 16].
Figure 2(a) represents a single stage RC ladder structure for designing a pseudo-capacitance of a particular fractional order(α) and figure 2(b) shows an equivalent RC tree formed by cascading many such individual single stage RC networks as in figure 2(a) for better approximations of frequency and phase over a particular frequency range.

RC Ladder component values generation.

Fractional order capacitors are generated for various orders; both fractance and their frequency response curves are studied herewith. This is done to ensure whether the designed pseudo-capacitances have fractional behavior or not in a desired frequency and phase spectrum. Figure 3 depicts a RC ladder of n equivalent stages. The values of resistors and capacitors of the progressive ladder structure vary based on the fractional order, α, for which the fractance has been designed (keeping the pseudo-capacitance value same). Keeping the fractance value same, magnitude curves have been plotted for different fractional orders, α ranging from 0.2 to 0.9, as can be seen in Figure 4. The simulated R and C values for the ladder network have also been taken for various fractional orders ranging from, α=0.2 to α=0.9. Table 1 depicts the ladder values for same fractance, F=10n, at different order, α varying from 0.2 to 0.9. Although, the pseudo-capacitance is same, that is F=10n, the design using different fractional order α offers different properties to the fractance device. FOCs offer a unique phase and frequency control by changing α, keeping the magnitude fixed.