Fractional Step Analog Filter Design
Published 2013 · Mathematics
Using the fractional Laplacian operator, s α , this chapter outlines the process to design, analyze, and implement continuous-time fractional-step lowpass, highpass, and bandpass filters of order (n + α), where (α) is the fractional-step between the integer orders with value 0 < α < 1. The design of these filters is done using transfer functions in the s-domain without solving fractional-order differential equations in the time domain. The design process, stability analysis, PSPICE simulations, and physical realization of these filters are presented based on minimumphase error approximations of the operator s α . Four methods of implementation, using fractional capacitors in the Tow-Thomas biquad, Single Amplifier Biquads (SABs), Field Programmable Analog Array (FPAA) hardware and Frequency Dependent Negative Resistor (FDNR) topologies to realize decomposed transfer functions are demonstrated.