Degree, ripple, and transition width of elliptic filters

Author

Vlcek, Miroslav ; Unbehauen, Rolf

Author_Institution

Lehrstuhl fur Allgemeine und Theor. Elektrotech., Erlangen-Nurnberg Univ., West Germany

Volume

36

Issue

3

fYear

1989

fDate

3/1/1989 12:00:00 AM

Firstpage

469

Lastpage

472

Abstract

Simple analytic formulas inverting the degree education in both analog and digital equiripple filter approximations are presented. The inversion of the degree equation which is usually expressed as a ratio of theta functions, known in classical mathematics as a modular equation, is obtained in form of a finite product of Jacobian functions. From the numerical point of view it allows the recalculation of the parameters which control the optimization using an efficient arithmetic-geometric-mean procedure only. For the evaluation of k/sub 1/ from n and K (k´, respectively) the zeros of the characteristic function are used and no additional computation is required.<>

Keywords

digital filters; filters; transfer functions; Jacobian functions; analog; characteristic function; degree equation; digital; efficient arithmetic-geometric-mean procedure only; elliptic filters; equiripple filter approximations; finite product; modular equation; theta functions; transition width; Charge measurement; Chebyshev approximation; Current measurement; Equations; Filters; Jacobian matrices; MOS capacitors; Measurement standards; Solid state circuits; Switching converters;

fLanguage

English

Journal_Title

Circuits and Systems, IEEE Transactions on

Publisher

ieee

ISSN

0098-4094

Type

jour

DOI

10.1109/31.17602

Filename

17602