Traditional continuous-time filters are of integer order. However, using fractional calculus, filters may also be represented by the more general fractional-order differential equations in which case integer-order filters are only a tight subset of fractional-order filters. In this work, we show that low-pass, high-pass, band-pass, and all-pass filters can be realized with circuits incorporating a single fractance device. We derive expressions for the pole frequencies, the quality factor, the right-phase frequencies, and the half-power frequencies. Examples of fractional passive filters supported by numerical and PSpice simulations are given. © 2008 World Scientific Publishing Company.
Design equations for fractional-order sinusoidal oscillators: Four practical circuit examples
Four practical sinusoidal oscillators are studied in the general form where fractional-order energy storage elements are considered
Fractional-order sinusoidal oscillators: Design procedure and practical examples
Sinusoidal oscillators are known to be realized using dynamical systems of second-order or higher