Realisation of nth-order indefinite RC admittance matrices

A new and systematic technique has been developed for the realisation of nth-order-indefinite admittance matrices as earthed structures by the 2-element-type networks that are without any transformer. There is no restriction on the number of permissible poles present in the admittance matrices. The technique is based on suitably partitioning the residue matrices, and sharing them with the other terms present in the indefinite admittance matrix, so that each partition yields a realisable network on inversion. The necessary and sufficient conditions for this type of realisation have been stated, and the relevant theorem is proved. The technique is definite, and simple. It has a great utility for multiport-transfer-function synthesis. Numerical examples have been given to illustrate the synthesis procedure.