Generalized Fully Adjustable Structure for Emulating Fractional-Order Capacitors and Inductors of Orders less than Two

Abstract

A novel scheme suitable for the emulation of fractional-order capacitors and inductors of any order less than 2 is presented in this work. Classically, fractional-order impedances are characterized in the frequency domain by a fractional-order Laplacian of the form $$s^{\pm \alpha }$$ with an order $$0<\alpha <1$$. The ideal inductor and capacitor correspond, respectively, to setting $$\alpha =\pm 1$$. In the range $$1<\alpha <2$$, fractional-order impedances can still be obtained before turning into a Frequency- Dependent Negative Resistor (FDNR) at $$\alpha =\pm 2$$. Here, we propose an electronically tunable fractional-order impedance emulator with adjustable order in the full range $$0<\alpha <2$$. The values of the emulated capacitance/inductance, as well as the bandwidth of operation, are also electronically adjustable. The post- layout simulation results confirm the correct operation of the proposed circuits.