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In this research, the analysis of the active circuit in the fractional domain has been performed by using the fractional differential equation approach where the measurability in time dimension of the derivative term has also been concerned unlike the previous work. The OTA-C filter has been adopted as the candidate active circuit due to its compactness and capability to serves as the fundamental building block of more complicated circuits. The derivative term of the fractional differential equation which includes the fractional time component parameters for obtaining such time dimensional measurability has been interpreted in Caputo sense, and the analytical solution of such an equation has been determined with the aid of Laplace transformation. With the obtained solution, the time dimensional measurability aware fractional derivative based circuit responses to various inputs have been determined, the circuit fractional time constant and other crucial time parameters have been determined and the temporal behaviour of the circuit has been analysed in the fractional domain. The loci of the pole on W-plane has been determined and the stability analysis has also been presented. Moreover, we also mathematically prove that the OTA-C filter in the fractional domain can be electronically realized with time dimensional measurability awareness by using a state of the art fractional capacitor.

The Time Dimensional Measurability Aware FDE Based Analysis of Active Circuit in The Fractional Domain