Approximated Fractional-Order Inverse Chebyshev Lowpass Filters

In this paper we use a least-squares fitting routine to approximate the stopband ripple characteristics of fractional-order inverse Chebyshev lowpass filters which have fractional-order zeros and poles. MATLAB simulations of $$(1+\alpha )$$(1+α)-order lowpass filters with fractional steps from $$\alpha =0.1$$α=0.1 to $$\alpha =0.9$$α=0.9 are given as examples. SPICE simulations of 1.2-, 1.5-, and 1.8-order lowpass filters and experimental results of a 1.5-order filter using approximated fractional-order capacitors in a Multiple-Input Biquad circuit validate the implementation of these circuits.

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