Fractional order two port network oscillator with equal order

Abstract

Most of electric circuits can be viewed as a two port network with two terminals defined as input and output ports. In this paper, two different concepts are combined together which are the two port network concept and the fractional calculus to design a general fractional order two port network with equal order. An oscillator case study with three impedances structure has been presented. The three impedances are two equal order fractional capacitors and a resistor. Two different two port network are studied which are Op-amp based circuit and nonideal gyrator circuit. The general oscillation frequency and condition for each case have been derived and discussed numerically using Matlab. Spice simulations are presented for some cases to validate the proposed idea where the fractional order oscillator has more degrees of freedom than the integer order.