Practical Realization of Tunable Fractional Order Parallel Resonator and Fractional Order Filters

This paper introduces a tunable fractional order parallel resonator (FOPR) whose resonating frequency can be tuned by the coefficient of a fractional order (FO) element (fractor). At the same time, its Q-factor can be set very high (theoretically infinite) by varying its resistor. Using this FOPR circuit, two simple FO filters (FO bandpass and FO notch) are also developed. The paper includes detail sensitivity analyses of these circuits for various circuit parameters and describes how different design parameters of proposed FOPR and FO filters are chosen accordingly. Proposed FOPR and FO filters are simulated in MATLAB and realized in hardware. The hardware circuits are tested practically, and detail experimental results are provided. It is found that the experimental data are in good agreement with the simulation data. In hardware, the realized FOPR has achieved a Q-factor up to 360, and the realized FO notch filter has Q > 10 when its attenuation is more than 30 dB. Different practical aspects of filter tuning are also described in detail.