Fractional Step Analog Filter Design

  • Todd FreebornEmail author
  • Brent Maundy
  • Ahmed Elwakil
Part of the Lecture Notes in Electrical Engineering book series (LNEE, volume 233)


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.


Fractional calculus Fractional filters Analog circuits 


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.University of CalgaryCalgaryCanada
  2. 2.University of SharjahSharjahUnited Arab Emirates

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