On the explicit formulas for the elements in low-pass ladder filters

To aid in searching explicit formulas for the elliptic-function filter, formulas are developed by which the elements of a resistively terminated, linear low-pass LC ladder filter can be expressed in terms of the filter´s natural frequencies as well as its loss poles and zeros. After a general approach to the problem, a special case illustrates the formulas. It is shown that the development of the Orchard´s determinants with the help of the Newton´s formulas allowed the derivation of expressions for filter elements involving the sums of the powers of the poles and zeros of the reflection coefficient