Stability Analysis of Fractional-Order Filters Realized with PMMA Coated Elements
Kumar Biswal, Sanjeeb Kumar Kar, Madhab Chandra Tripathy
Abstract
The initial work in this paper discusses the concept of stability of a circuit by transforming s-plane to F-plane and W-plane. This article also describes an approach to realize fractional-order active filters using fractional-order elements and studied its output voltage stability over a frequency range. The filters' response in both low and high frequency range have been simulated in P-Spice and Matlab for comparison with experimental results. Both low-pass and high-pass filters incorporate two capacitors which are used as non-integer (i.e. fractional) devices. This requires two fractional capacitors with orders <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\alpha$</tex> and <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$\beta(0 < \alpha,\ \beta\leq 1)$</tex> . The outputs of the two proposed filters shown in frequency domain were obtained experimentally and have been compared with simulated results using MATLAB and P-Spice toolbox. This simulation was carried out by taking fractional-order element which is approximated with a Domino Ladder network representation.