Design of Asymmetric Slope Fractional Band Reject Filters

Abstract

In this work, we propose new techniques of designing asymmetric-slope band reject filters. Two new non-conventional transfer functions are presented based on the concept of fractional Laplacian operator, s^(α) where 0 < α < 1. It is possible to achieve asymmetric slopes, large values of notch magnitude up to 90 dB and high Q values for appropriate values of α using these filters. In addition, unlike integer order filters, independent control of slopes above the notch frequency can be achieved by simply changing the values of α. Different circuit realization techniques based on fractional floating inductor, multiple amplifier biquad (MAB) and field programmable analog array (FPAA) are also presented. The operation of these circuits is verified by plotting PSPICE simulation results for different values of α and showing its comparison with experimental results.