Cascade Synthesis of Distributed RC Networks

The synthesis of simultaneously prescribed drivingpoint and transfer admittances for distributed RC networks without transformers is considered. Realizations with common ground connections are required. The realizations given, in general, involve an arbitrary multiplying constant for the transfer admittance and are valid except when the prescribed transmission zeros, t = \tanh \sqrt{p} = \delta_{0} + j \omega_{0} are such that \omega_{0}^{2} \delta_{0}^{2} 1 + \omega_{0}^{2} . If only the short-circuit transfer admittance y_{12} or the open-circuit voltage transfer ratio T_{12} is specified, a realization using surplus factors is given valid for all transmission zeros other than real zeros less than unity, which can never be realized by an unbalanced commensurate distributed RC network, and that for such networks, zeros of transmission where \delta_{0}^{2} >\omega_{0}^{2} + (\delta_{0}^{2} + \omega_{0}^{2})^{2} always require the use of surplus factors. Examples of the various synthesis procedures are given.