Fractional order oscillator with independent control of phase and frequency

This paper generalizes the concept of the oscillators based on the operational transresistance amplifier (OTRA) into the fractional order domain. The added parameter in the fractional-order design is an important in practical and can model the non-ideality of the conventional capacitors. The general condition and frequency of oscillation have been derived analytically in terms of the circuit components and the fractional order parameters. Different special cases are introduced based on the extra fractional-order parameters in which some features are appeared in the fractional-order circuit only. Through the proposed circuit, the phase and frequency can be controlled individually via the fractional order parameters. Numerical and Spice simulation results of different fractional-order oscillators are presented to validate the analytical formulas.