Elliptic functions in network synthesis

Abstract Admittedly the Jacobian elliptic functions are not too familiar to the engineer, However, there are occasions when alternate technique are not as direct or as convenient to solve the approximation problem of network synthesis. The role of elliptic functions in providing a common thread for fundamental concepts involved in Cauer image parameter filters, filters on an insertion loss basis and wide band 90° phase-difference networks is shown. A “unified” design chart for these networks is also included. Additional tabular and graphical data are presented emphasizing extreme parameter values not found in the literature, that is, modular angle θ > 89°, to facilitate getting numerical results. An attempt has been made to provide a practical basis for engineering insight into the synthesis problem. It is also hoped that this paper may serve as an inducement to some of the engineers interested in network synthesis to acquire broader acquaintance with these topics via the references cited.

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