Showing papers on "Network theory published in 1967"

Computer methods of network analysis

Abstract: In this tutorial paper, the influence of the computer not only on the modus operandi of circuit design, but also on network theory itself, is discussed. The topological properties of linear graphs are reviewed and a matrix-topological formulation of the network problem is described. In addition to the classical mesh, node, and cutset methods, a mixed method of analysis is described which is applicable to dc, ac, and transient problems. Numerical methods of solving linear and nonlinear dc network problems are discussed and a new approach to ac analysis, using the mixed method and a numerical solution of the matrix eigenvalue problem, is described. The extension of this method to the transient analysis of linear networks is also explained. Finally, the problem of instability in the numerical integration of differential equations is discussed and several means of solving the problem are outlined.

Network theory without circuit elements

Abstract: Network methods are by no means limited to lumped systems. Once the ports of a generalized physical structure are defined by use of a modal decomposition of signals, the structure can be analyzed using network techniques which extend beyond the domain of RLC systems and rational network functions. If the physical system is observed as a black box at its ports and various physical time-domain postulates such as linearity, energy, and power conservation theorems are applied in network terms, a variety of realizability relations are obtained for linear, passive, time-invariant structures. For example, one is led to generalizations of bounded real and positive real functions for distributed systems. The network technique also results in a number of interesting theorems for lossless structures such as a generalization of Foster's reactance theorem, and restrictions on minimum phase realizability, and on signal transmission and group delay in distrributed, lossless networks. These results apply in structures containing gyrotropic, dispersive media as well as in the reciprocal, nondispersive case.

Computer methods of network analysis

Abstract: This is a tutorial paper which highlights the influence of the computer not only on the modus operandi of circuit design but also on network theory itself. It reviews the topological properties of linear graphs and describes a matrix-topological formulation of the network problem. In addition to the classical mesh, node, and outset methods, a mixed method of analysis is described which is applicable to d-c, a-c, and transient problems.Numerical methods of solving linear and non-linear d-c network problems are discussed and a new approach to a-c analysis, using the mixed method and a numerical solution of the matrix eigenvalue problem, is described. The extension of this method to the transient analysis of linear networks is also explained. Finally, the problem of instability in the numerical integration of differential equations is discussed and several means of solving the problem are outlined.

Unified theory on topological analysis of linear systems

Abstract: Topological formulas were stated by Kirchhoff for mesh equations, by Maxwell for nodal equations, by Mason for signal-flow graphs and by Coates for flow graphs. In the paper, it is shown that all these formulas can be obtained from one another. Using these relationships, a generalised star-mesh transformation in network theory is obtained. Simple ways of drawing these associated directed graphs from a given network and illustrative examples are also given.

An introduction to on-line circuit design

Abstract: This paper identifies and introduces in simple terms a broad view of on-line circuit design, which reflects the interrelation and relevance of several diverse areas such as network theory, linguistics, numerical analysis, programming systems, and on-line computation. Discussion is presented in terms of 1) the structure of on-line utlities, 2) requirements imposed by the interactional nature of on-line circuit design, 3) program structures (data structures), and 4) network-analysis considerations. A brief set of conclusions is given.

Connection between network theory and the theory of linear dynamical systems

Abstract: A connection is established between network theory and the theory of linear dynamical systems which may provide a convenient way of formulating network problems for solution by digital computer and may also permit a new approach to some problems in network theory.