Some explicit formulas for the components in low-pass ladder networks

The paper gives explicit formulas for the component values in a general low-pass ladder filter in terms of the coefficients of the polynomials of the open- or short-circuit input impedance and of the frequencies of infinite loss. The formulas are a direct generalization of the results given by Bader in: 1940 for the special case where all the loss poles are at infinite frequency and use determinants that are natural extensions of those due to Hurwitz. An alternative representation of these determinants has been found in the form of a double bialternant that provides a link with some recent work by Navot. One motivation for presenting these various formulas is the hope that they will help in discovering the explicit formulas for the elliptic-function filter.