Stability Improvement of Fractional-Order Filters Using Gain Bandwidth and Step Response Approach

Abstract

AbstractThis article focuses on the stability of fractional-order filter circuits, which are characterized by transfer function and their common characteristic equations. Two methods such as gain bandwidth and step response approach are adopted to analyze the transition bandwidth by varying the exponent (order) of fractional capacitor used in filter circuit. The exact analytical solutions are derived for low-pass, high-pass and band-pass filters with different orders of capacitor. The characteristic equation and transfer function of these filters are presented along with simulation results. Here, the stability analysis is presented by considering the bandwidth and step response of the fractional-order filters. Since the bandwidth of the filter is expressed in terms of cutoff frequency which further changes with variation in exponent (order) of capacitor, it is considered for filter circuit in simulation results. Secondly, the steadiness of low-pass filter’s response to a step response input is analyzed keeping its DC gain constant for this filter with variable order of capacitor. The response of the filter becomes stable when the exponents of the capacitor are fractional numbers, then compared with that of integer-order filter.KeywordsFractional calculusFractional-order filterGain-bandwidthStep responseTransfer function