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

Abstract

In this research, the analysis of the active circuit in the fractional domain has been performed by using the fractional differential equation approach where themeasurability 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 renown. 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 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 has been determined and thetemporal 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 proof that the OTA-C filter in the fractional domain can be electronically realized with time dimensionalmeasurability awareness by using the state of the art fractional capacitor.