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A chebyshev rational function with low Q ‐factors
Author(s) -
Rabrenović D.,
Lutovac M.
Publication year - 1991
Publication title -
international journal of circuit theory and applications
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.364
H-Index - 52
eISSN - 1097-007X
pISSN - 0098-9886
DOI - 10.1002/cta.4490190303
Subject(s) - chebyshev filter , mathematics , rational function , chebyshev polynomials , chebyshev nodes , elliptic rational functions , chebyshev equation , transfer function , polynomial , function (biology) , elliptic function , ideal (ethics) , connection (principal bundle) , pure mathematics , mathematical analysis , orthogonal polynomials , elliptic curve , classical orthogonal polynomials , quarter period , geometry , philosophy , epistemology , evolutionary biology , electrical engineering , biology , engineering
Abstract The presented rational function is a modification of a recently published Chebyshev rational function defined by means of some orthogonal polynomials. the necessary conditions providing for the lowest pole Q ‐factors for a given ripple are found. the function is a ratio of two similar Chebyshev polynomial transfer functions with multiple poles. The selectivity of the function can be increased by using the Chebyshev rational characteristic function instead of the characteristic polynomials. the minimum number of active elements in the cascade connection is obtained with third‐order elliptic characteristic functions. The function is compared with the Cauer (elliptic) and MCPER filters. the distinctive features of the presented function are small Q ‐factors of the poles, almost ideal dynamic range, simple design and poles with the same multiplicity m , where m designates the number of cascaded blocks.