Design and Performance Study of Dynamic Fractors in Any of the Four Quadrants

A fractor is a simple fractional-order system. Its transfer function is (1/Fs^{alpha }); the coefficient, F, is called the fractance, and (alpha ) is called the exponent of the fractor. This paper presents how a fractor can be realized, using RC ladder circuit, meeting the predefined specifications on both F and (alpha ). Besides, commonly reported fractors have (alpha ) between 0 and 1. So, their constant phase angles (CPA) are always restricted between (0^{circ }) and (-90^{circ }). This work has employed GIC topology to realize fractors from any of the four quadrants, which means fractors with (alpha ) between (-)2 and +2. Hence, one can achieve any desired CPA between (+180^{circ }) and (-180^{circ }). The paper also exhibits how these GIC parameters can be used to tune the fractance of emulated fractors in real time, thus realizing dynamic fractors. In this work, a number of fractors are developed as per proposed technique, their impedance characteristics are studied, and fractance values are tuned experimentally.