Energy Consideration of a Capacitor Modelled Using Conformal Fractional Order Derivative

Abstract

Fractional order circuit elements have become important parts of electronic circuits to model systems including supercapacitors, filters, and many more. The conformal fractional derivative (CFD), which is a new basic fractional derivative, has been recently used to model supercapacitors successfully. It is essential to know how electronic components behave under excitation with different types of voltage and current sources. A CFD capacitor that is not a well-known element and its usage in circuits are barely examined in the literature. In this research, it is examined how to calculate the stored energy of a CFD capacitor with a series resistor supplied from a DC voltage source. The solutions given in this study may be used in circuits where supercapacitors are used.