Synthesis of optimum RC phase-shift network

This paper is concerned with the following problem. Given two terminating resistances R, and R0, design a low-pass ladder RC network of n sections such that the magnitude of the transfer-voltage ratio is minimized at a given phaseshift and at a given frequency . This problem is solved explicitly. It was found that the optimum phase-shift network is a geometrical progression network properly terminated at both ends. In the distributed case ( approaches infinity), the optimum network is an exponentially tapered line, terminated by four lumped impedances.