Approximated fractional order Chebyshev lowpass filters (Q1666699)

Summary: 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.