Realizing Fractional Capacitor for the
Proposed Oscillator
Designing
The work on realizing the fractional order capacitors is going on since
decades [7-9], however, still they are not available on a commercial
scale. Various approximation techniques are being considered to depict
the fractional characteristics in a circuit. For a fractional capacitor,
the impedance can be represented as:
\begin{equation}
Z\left(\text{jw}\right)=\frac{1}{C{(jw)}^{\alpha}}\nonumber \\
\end{equation}\begin{equation}
Z\left(s=jw\right)=\frac{1}{Cs^{\alpha}}\nonumber \\
\end{equation}This expression has a constant phase which equals to (–απ/2) and is
dependent upon α, the fractional order. Therefore a close optimization
network is required to be designed that closely mimics this behavior.
Fractional order capacitors are approximated by using a geometrically
progressive RC ladder structure. These structures are used to implement
tank circuits with low phase shift and are used to create fractional
order oscillators. The LC circuits built using these capacitors are
tested using AC sweeps in order to create Bode plots and verify
fractional order reactance [32]. The only drawback is that the huge
network comprising of R and C of different values tends to increase the
economic cost and space occupied by these ladder circuits.