Figure 10: Bode plot for integer order CO with (a) L=100pH and (b)
L=1pH.
Figure 10 shows the Bode plot, showing both the phase and magnitude, for
the integer order CO with different Ls, L=100pH and 1pH. At the
intersection of magnitude and phase plots, the x-axis gives the
frequency of oscillation, as can be seen in Figure 10 (a,b). However,
with conventional integer order CO the oscillation frequency for the
same set of parameters remains fixed. Both magnitude and phase curves
follow a conventional pattern at certain values of circuit parameters.
This led to the replacement of integer order theory with robust
fractional order theory. Fractional order elements allow efficient
control over phase, magnitude and frequency of the designed circuit.
Keeping the component values same and varying the fractional order α
generates different results. This allows more design freedom and
captures the real analysis paradigm since most of the things have a
fractional chaotic behavior.
Fractional order MOSFET based
Colpitts
Oscillator
Fractional circuit can be designed by replacing one or more capacitors
with fractance devices of known value and a certain fractional order, α.