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

摘要

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.