Figure 12: AC responses of pseudo-capacitance 0.3n for different α.
The designing of FOCs is validated by the presence of their constant
phase zones (CPZ). It has been observed that the fractance devices show
constant or near constant behavior in terms of phase shift for the
entire frequency band [32]. Figure 12 shows the constant phase zones
of pseudo-capacitance 0.3n for orders 0.45, 0.52, 0,67 and 0.74. The
plots show that other than a small ripple zone, the phase remains
constant over most part of the frequency spectrum. The CO with
C1=C2=0.3n in the integer domain gave oscillation frequency of 1.2GHz
(simulated) with 100pH inductor. However, the same value of
pseudo-capacitance, i.e. 0.3n with fractional order 0.4 results in a
transient of oscillation frequency 1.7GHz. Further, by varying α with
the same numerical value of capacitance generates plots of different
frequency, thereby offering an extra degree of freedom in fractional
calculus.