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In Figure 15, the two capacitors have been replaced by FOCs of different order.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.