Realization of a Constant Phase Element and Its Performance Study in Differentiator and Integrator Circuits

Frakcionalni račun je grana matematike koja se bavi diferenciranjem i integriranjem necjelobrojnog reda. Istraživači u području elektrokemije izvijestili su o konstantnoj fazi (engl. constant phase - CP) ponašanja sučelja metal-izolator-otopina. Koncepti frakcionalnog računa su našli primjenu i u inženjerstvu. U ovom radu realizirao se element s konstantnom fazom (CPE). Pritom su provedena mjerenja pomoću dielektrične spektroskopije na elektrodama uronjenim u otopinu i u voće u svrhu realizacije CPE. Tako realizirani CPE opisan je pomoću Cole-Cole modela, odnosno izmjereni i izračunati su mu parametri. Dobiveni element upotrijebljen je na primjeru frakcionalnog derivatora te na električni filtar s necjelobrojnog reda. Naveden je odziv necjelobrojnog sustava. Uspoređen je električni filtar necjelobrojnog reda s cjelobrojnim.Fractional calculus is a branch of mathematics dealing with differentiation and integration to non-integer order. Researchers in the field of electrochemistry have reported about the constant phase (CP) behavior of metal–insulator–solution interface. Fractional calculus can be found in diverse fields of engineering. In this paper, a constant phase element (CPE) is to be realized. Firstly, measurements were made using dielectric spectroscopy on probes immersed in liquid medium and in fruit for the CPE realization. The CPE thus realized was described using the Cole-Cole model (had his parameters measured and calculated). The resulting element was used in fractional differentiator and in electronic filter of non-integer order. Response of a non-integer order system was measured. Electronic filter of non-integer order was compared to integer-order filter