Filters approximating ideal amplitude and arbitrary phase characteristics

Author

Rhodes, John David

Volume

Issue

fYear

1973

fDate

3/1/1973 12:00:00 AM

Firstpage

120

Lastpage

124

Abstract

The closed-form solution is derived for the scattering transfer function $S_{12}(p)$ of a resistively terminated lossless reciprocal two-port prototype network of degree $2n$ which satisfies the following constraints: $|S_{12}(j\\omega ) | \\leq 1$ $|S_{12}({\\pm}j{\\omega }_i) | = 1 , i = 1 \\rightarrow n$ $\\arg S_{12}({\\pm}j{\\omega }_i) = \\pm \\psi({\\omega }_i), i = 1 \\rightarrow n$ where the $\\omega _i$ are arbitrary and $\\psi(\\omega )$ is any odd function. The solution is obtained in terms of the arbitrary phase polynomials of the first and second kinds, which are capable of being generated through simple recurrence formulas.

Keywords

Filters; Linear-phase filters; Maximally-flat-amplitude filters; Chirp modulation; Frequency modulation; Linear approximation; Linearity; Microwave filters; Phase distortion; Phase modulation; Polynomials; Prototypes; Transfer functions;

fLanguage

English

Journal_Title

Circuit Theory, IEEE Transactions on

Publisher

ieee

ISSN

0018-9324

Type

jour

DOI

10.1109/TCT.1973.1083626

Filename

1083626

Link To Document

https://search.isc.ac/dl/search/defaultta.aspx?DTC=49&DC=1171805