Abstract
In the control and protective circuits of complex electrical systems it is frequently necessary to make intricate interconnections of relay contacts and switches. Examples of these circuits occur in automatic telephone exchanges, industrial motor-control equipment, and in almost any circuits designed to perform complex operations automatically. In this article a mathematical analysis of certain of the properties of such networks will be made. Particular attention will be given to the problem of network synthesis. Given certain characteristics, it is required to find a circuit incorporating these characteristics. The solution of this type of problem is not unique and methods of finding those particular circuits requiring the least number of relay contacts and switch blades will be studied. Methods will also be described for finding any number of circuits equivalent to a given circuit in all operating characteristics. It will be shown that several of the well-known theorems on impedance networks have roughly analogous theorems in relay circuits. Notable among these are the delta-wye (δ-Y) and star-mesh transformations, and the duality theorem.
Keywords
RelayElectronic circuitNetwork analysisComputer scienceTopology (electrical circuits)Equivalent circuitDuality (order theory)Electrical networkElectronic engineeringElectrical engineeringMathematicsEngineeringVoltagePower (physics)PhysicsDiscrete mathematics
Affiliated Institutions
Related Publications
CXVII. Some general theorems for non-linear systems possessing reactance
Summary The theorems and concepts presented here are generally applicable to circuits of electrical or mechanical elements with non-linear characteristics. The quantity called t...
Elements of Algebraic Topology
Elements of Algebraic Topology provides the most concrete approach to the subject. With coverage of homology and cohomology theory, universal coefficient theorems, Kunneth theor...
Computing with Neural Circuits: A Model
A new conceptual framework and a minimization principle together provide an understanding of computation in model neural circuits. The circuits consist of nonlinear graded-respo...
Relative Sensing Networks: Observability, Estimation, and the Control Structure
In this paper we consider various structural aspects of estimation and control over relative sensing networks. We first expand on our earlier characterization of equivalent sens...
Duality Results for Conic Convex Programming
textabstractThis paper presents a unified study of duality properties for the problem of minimizing a linear function over the intersection of an affine space with a convex cone...
Publication Info
- Year
- 1938
- Type
- article
- Volume
- 57
- Issue
- 12
- Pages
- 713-723
- Citations
- 1008
- Access
- Closed
External Links
Social Impact
Altmetric
PlumX Metrics
Social media, news, blog, policy document mentions
Citation Metrics
1008
OpenAlex
Cite This
Claude E. Shannon
(1938).
A symbolic analysis of relay and switching circuits.
Transactions of the American Institute of Electrical Engineers
, 57
(12)
, 713-723.
https://doi.org/10.1109/t-aiee.1938.5057767
Identifiers
- DOI
- 10.1109/t-aiee.1938.5057767