Topological degrees of freedom and mixed analysis of electrical networks
- 1 November 1970
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Transactions on Circuit Theory
- Vol. 17 (4) , 491-499
- https://doi.org/10.1109/TCT.1970.1083186
Abstract
A new concept of topological degrees of freedom is introduced as a generalization of the concepts of rank and nullity. This number.corresponds to the minimum number of independent variables taken in mixed analysis of electrical networks, which is a generalization of well-known node-pair and loop analysis. An explicit formula giving topological degrees of freedom and a graph-theoretical algorithm for finding all the minimum sets of independent variables are presented. Another new concept of extremal tree is introduced and shown to play a central role in obtaining the results.Keywords
This publication has 1 reference indexed in Scilit:
- State-Variable Analysis of RLC Networks Containing Nonlinear Coupling ElementsIEEE Transactions on Circuit Theory, 1969