Approximated Fractional Order Chebyshev Lowpass Filters

We propose the use of nonlinear least squares optimization to approximate the passband ripple characteristics of traditional Chebyshev lowpass filters with fractional order steps in the stopband. MATLAB simulations of (1 + alpha), (2 + alpha), and (3 + alpha) order lowpass filters with fractional steps from alpha = 0.1 to alpha = 0.9 are given as examples. SPICE simulations of 1.2, 1.5, and 1.8 order lowpass filters using approximated fractional order capacitors in a Tow-Thomas biquad circuit validate the implementation of these filter circuits.