Material performance measurement of a promising circuit element: fractor-part I: driving-point impedance function of the arbitrary-order fractor in its natural implementation

Abstract

Here and in the companion paper, the physical performance measurement, especially measurement units and physical dimensions of fractance and rules for fractors in series and parallel are discussed. The concept of fractance, as the fractional-order impedance of a fractor, arose following the successful synthesis of a fractional differentiator in an analogue circuit. Until now, however, the measurement units and physical dimensions of fractance have not been proposed. Motivated by this need, in this paper, I studied the electrical properties of fractor. In particular, the driving-point impedance function of the arbitrary-order fractor in its natural implementation is introduced. Through mathematical and physical analysis, the driving-point impedance function of the 1/2-order fractor is studied, following which the driving-point impedance function of the arbitrary-order fractor is proposed. This paper discusses fundamental issues, whereas Part II is devoted to the measurement units and physical dimensions of fractance and the rules for fractors in series and parallel.