On the Synthesis of R Networks
- 1 March 1961
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IRE Transactions on Circuit Theory
- Vol. 8 (1) , 31-39
- https://doi.org/10.1109/tct.1961.1086745
Abstract
A study is made of a class of real symmetric matrices, and a new set of necessary and sufficient conditions are defined on the entries of these matrices such that they can be synthesized, without using ideal transformers, as an R-network with a minimum number of terminals. The conditions are stated in terms of the terminal graph used in representing the terminal characteristics of multiterminal components. The new class of matrices then represents "terminal equations" corresponding to a path-tree terminal graph. It is also shown that one of the well-known class of matrices, referred to as dominant matrices, represent the terminal equations for a Lagrangian-tree terminal graph. It is further indicated that any such class of real symmetric matrices is distinguishable by a particular terminal graph. For the cases when a real symmetric matrix of order n cannot be synthesized by anRnetwork with(n + 1)terminal vertices, an "enlarged" matrix is formed, and the necessary and sufficient conditions for realizability of these matrices are given.Keywords
This publication has 4 references indexed in Scilit:
- Applications of matrix algebra to network theoryIEEE Transactions on Information Theory, 1959
- Conditions for the impedance and admittance matrices of n-ports without ideal transformersProceedings of the IEE Part C: Monographs, 1958
- On Networks without Ideal TransformersIRE Transactions on Circuit Theory, 1956
- R -Matrices and Equivalent Networks. IJournal of Mathematics and Physics, 1937