A NECESSARY CONDITION FOR WYE-DELTA TRANSFORMATION
Abstract
Let the binary operations and denote the arithmetic operations of addition (a b = a + b) and reciprocal addition (a b = ab/(a + b)), that is, and are the series and parallel combination rules for resistor networks. It is easy to verify that the identity (1) (a b c) ((a b) (a c) (b c)) = (a b c) ((a b) (a c) (b c)) ;olds. Furthermore if the binary operation . denotes arithmetic multiplication then the identity (2) (a b) . (a b) = a . b holds. Now suppose only that and are associative commutative binary operations on an abstract set S and that there exists a commutative group R, . such that S is a subset of R and (2) holds on S. If in an abstract network theory and are the series and parallel combination rules and if wye-delta transformations are valid in this theory then it is shown that (1) must hold. Wye-delta transformations are valid for resistor networks but need not exist in resistor-inductor-capacitor (RLC) networks. Thus, in the presence of (2), identity (1) is a necessary but not sufficient condition for wye-delta transformation.
Document Details
- Document Type
- Technical Report
- Publication Date
- Mar 01, 1963
- Accession Number
- AD0403836
Entities
People
- Alfred Lehman
Organizations
- University of Wisconsin–Madison