Figure 14: The FFT plots for different fractional orders.
On analyzing the FFT plots, it has been observed that the oscillation
frequency tends to decrease slightly on increasing the fractional order,
being 1.68 GHz at α=0.4 and 1.351 GHz at α=0.81. Since the capacitor
being fractional of order α in the CO design, it results in a 2+α
circuitry. The designed fractional order CO has an order in the range
2<α<3. If both the capacitors are replaced by FOCs
of different orders it enables us to have a greater degree of freedom.
The replacement by a higher order FOC increases the system accuracy,
thus higher order systems in fractional domain are being considered.
Figure 15: Different orders fractional capacitances.
In Figure 15, the two capacitors have been replaced by FOCs of different
order. This results in C1=0.3n s-0.19 and C2=C3= 0.3
s-0.38 :
\begin{equation}
n=1+\frac{C_{2}+C_{3}}{C1}\nonumber \\
\end{equation}\begin{equation}
n=1+\frac{0.6}{0.3}\nonumber \\
\end{equation}\begin{equation}
n=3\nonumber \\
\end{equation}A higher tap ratio implies a greater feedback fraction in the oscillator
design. For the CO with different order FOCs, an analysis of transient
characteristics is performed by varying the inductor values, as shown in
Figure 16.