Designing of Fractional Order Inverse Chebyshev Low Pass Filter Using Particle Swarm Optimization

Abstract

The design of fractional order inverse Chebyshev low pass filter has been presented in this paper. The (1+α) order inverse Chebyshev filters have been designed by comparing the transfer function of fractional order low pass notch filter with the second-order inverse Chebyshev low pass filter. Particle swarm optimization has been utilized to derive the coefficients of the fractional-order filters by varying α from 0.1 to 0.9. The canonical forms of these filters have been realized using multiple input Biquad circuits. The value of circuit elements for each order has been derived. Further, the values for the equivalent RC ladder network of the constant phase element have been derived by fifth-order continuous fractional expansion for the orders 1.2, 1.5 and 1.8. The magnitude plots for the 1.2 and 1.8 order inverse Chebyshev low pass filter have been plotted in SPICE and the magnitude plot for the 1.8 order filter has been compared with PSO approximated plot to confirm the feasibility of the OP-Amp based realized circuit with a mean error of 0.495dB.