Explicit formulas for element values in elliptic function prototype networks

Abstract
Explicit formulas are derived for elliptic function prototype networks in a direct and simple manner without recourse to continued-fraction expansion techniques. The natural prototype for the - elliptic function filter incorporates the concept of frequency invariant reactances and impedance inverters from which relatively narrow bandwidth, bandpass, or bandstop filters may be readily derived using the reactance slope parameter method. Formulas are given for the general arbitrary gain case where the zeros of the reflection coefficient are located in one half-plane or equally distributed between the two half-planes, and the degenerate cases of maximum gain and operation from a zero impedance generator are specifically recovered. The corresponding results are also presented for the inverse Chebychev response.

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