Explicit Formulas for Tschebyscheff and Butterworth Ladder Networks

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Abstract
Green found the closed-form formulas for the element values in a resistance-terminated ladder network that has a maximally flat (Butterworth) or equal-ripple (Tschebyscheff) characteristic. The Green formulas apply only when all the zeros of the reflection coefficient ρ are chosen to lie in one half-plane. In this paper we present new formulas for the element values for the case in which the zeros of ρ are chosen to alternate in the left and right half-planes. These formulas apply for n odd, where n is the degree of the dominator of the transfer function, and for any nonzero ratio of the output to the input resistance. The networks obtained are related to the symmetrical ones given by Bennett's and Belevitch's formulas for matched networks.

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