Fractional order oscillators based on operational transresistance amplifiers

In this paper, a general analysis of the fractional order operational transresistance amplifiers (OTRA) based oscillator is presented and validated through eight different circuits which represent two classifications according to the number of OTRAs. The general analytical formulas of the oscillation frequency, condition as well as the phase difference are illustrated for each case and summarized in tables. One of the advantages of the fractional-order circuit is the extra degrees of freedom added from the fractional-order parameters. Moreover different special cases {α = β ≢ 1, β ≢ α = 1, α ≢ β = 1} are investigated where the conventional case α = β = 1 is included in all of them. Also, the effect of the fractional order parameter on the phase difference between the two oscillator outputs is presented which increases the design flexibility and controllability. The effect of the non-ideal characteristics associated with OTRA on the presented oscillator is also studied. A comparison between the fractional order oscillators with their integer order counterpart is also presented to verify the advantages of the added fractional order parameters. Numerical and spice simulations are given to validate the presented analysis. © 2015 Elsevier GmbH.