Generalised Christoffel-Darboux formula most directly applied in generating fully symmetric doubly resistively terminated LC lossless ladder filters

In this article, the approximation problem of a continuous analogue filter function of even and odd order is solved mathematically most directly applying the proposed generalised Christoffel-Darboux formula for two continuous orthogonal polynomials (Chebyshev first and second kind) on the equal fini...

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Bibliographic Details
Published in:International journal of electronics 2013-07, Vol.100 (7), p.942-958
Main Authors: Ciric, Dejan G, Pavlovic, Vlastimir D
Format: Article
Language:English
Subjects:
analog circuits
Analogue filters
Approximation
circuit synthesis
Circuits
Comparative analysis
Exact solutions
filters
frequency analysis
Ladders
Mathematical analysis
Mathematical problems
Polynomials
Reactance
Segments
signal processing
Tolerances
Citations: Items that this one cites
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Summary:In this article, the approximation problem of a continuous analogue filter function of even and odd order is solved mathematically most directly applying the proposed generalised Christoffel-Darboux formula for two continuous orthogonal polynomials (Chebyshev first and second kind) on the equal finite segment of orthogonality in a compact explicit representative form. A set of analytic expressions of the proposed formula for the representative examples of odd-orders is given. Additionally, these expressions are applied in generating new excellent class all pole low-pass prototype analogue filter functions of odd orders (7, 9, 11, and 13th order). Based on the generated functions, the fully symmetric doubly resistively terminated LC ladder filter networks are realised by Darlington realisation. The generated filters are analysed, and their characteristics are presented. The effects of finite tolerance of a critical reactance of these ladder filters on the filter characteristics are considered. The filters generated by the proposed formula show excellent properties and possess important advantages in comparison to the corresponding filters generated by other methods.
ISSN:0020-7217
1362-3060
DOI:10.1080/00207217.2012.727352