Fractal Calculus Analysis of a Non-Ideal Operational Amplifier Bandpass Filter

Abstract

Fractal calculus is a new branch of calculus that has been widely applied in many scientific disciplines, e.g., sub-diffusion, super-diffusion, spatial analysis, and electrical engineering. In the area of electrical engineering, the fractal calculus has been applied to the analysis of many electrical circuits and the modeling of memelement and inverse memelement under the effect of fractal time. However, to the best of our knowledge, there exists no application of the fractal calculus to the active electrical circuit. Therefore, for the first time, we apply the fractal calculus to the analysis of an active circuit under the effect of fractal time in this work. The operational amplifier (OPAMP)-based bandpass (BP) filter has been chosen as our candidate active circuit. For a complete analysis, the nonidealities of the OPAMP have been taken into account. It has been found that the filter exhibits a power law dynamic in the frequency domain due to the effect of fractal time without any usage of the fractional order circuit element. The influences of the OPAMP's nonidealities on both magnitude and phase of the nondifferentiable (ND) transfer function are comprehensively analyzed.