Design of sharp cutoff low-pass maximally flat RC-active filters by cascading third-order blocks

Abstract

Pairs of coincident <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j{\omega}</tex> -axis zeros are added to the multiple real root maximally flat (MURROMAF) approximation function for designing sharp cutoff low-pass <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">RC</tex> -active filters. Expressions for transfer function and cutoff slope are derived in terms of the order <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</tex> , the multiplicity of the real pole <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">\mu</tex> , the number of pairs of <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">j{\omega}</tex> -axis zeros <tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</tex> and their locations. A design example is also given to illustrate the procedure for finding out the best transfer function.