Fractional resonance-based \(RL_{\beta}C_{\alpha}\) filters (Q474576)

Summary: We propose the use of a fractional order capacitor and fractional order inductor with orders \(0\leq \alpha,\beta\leq 1\), respectively, in a fractional \(RL_{\beta}C_{\alpha}\) series circuit to realize fractional-step lowpass, highpass, bandpass, and bandreject filters. MATLAB simulations of lowpass and highpass responses having orders of \(\alpha+\beta=1.5\) and \(1.9\) and bandpass and bandreject responses having orders of 1.5 and 1.9 are given as examples. PSPICE simulations of 1.1, 1.5, and 1.9 order lowpass and 1.0 and 1.4 order bandreject filters using approximated fractional order capacitors and fractional order inductors verify the implementations.