Impedance Synthesis of n-port Networks

Abstract

The realization of transformerlesa 4 networks is an outstanding unsolved problem in the field of network theory* Great attention has been paid to realize a short circuit conductance matrix by a resis-tive n-port network. On the other hand, the problem of realizing an open circuit impedance matrix has been given much less attention. This dissertation i completely devoted to the realisation of an open circuit nth order impedance matrix by an n-port network containing only positive resistors and having a star-port configuration, i.e. in which all the ports have a common datum. A method is developed to realize the open circuit impedance matrix of a resistive n-port network. A method, known as 'Fivotal Condensation' , to progress-ively reduce the order of given matrices is gainfully employed for this purpose. The given matrix is reduced to a set of second order matrices by snort circuiting appropriate, node pairs and these spend order matrices which give rise to a number of Pi networks are then used to realize the original nth order matrix. Some necessary and sufficient conditions are also mentioned. The method is illustrated by suitable examples. A brief remark about its application to a class of RLC networks is also included and illustrated by a simple example. The results of this dissertation are believed to yield a simple method for the realization of open circuit iMpedance matrices with star-port structure