Effect of Different Approximation Techniques on Fractional-Order KHN Filter Design

Having an approximate realization of the fractance device is an essential part of fractional-order filter design and implementation. This encouraged researchers to introduce many approximation techniques of fractional-order elements. In this paper, the fractional-order KHN low-pass and high-pass filters are investigated based on four different approximation techniques: Continued Fraction Expansion, Matsuda, Oustaloup, and Valsa. Fractional-order filter fundamentals are reviewed then a comparison is made between the ideal and actual characteristic of the filter realized with each approximation. Moreover, stability analysis and pole movement of the filter with respect to the transfer function parameters using the exact and approximated realizations are also investigated. Different MATLAB numerical simulations, as well as SPICE circuit results, have been introduced to validate the theoretical discussions. Also, to discuss the sensitivity of the responses to component tolerances, Monte Carlo simulations are carried out and the worst cases are summarized which show good immunity to component deviations. Finally, the KHN filter is tested experimentally.

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