access icon free Dual relations and the branch-dualising rule of the duality principle

© The Institution of Engineering and Technology
Received 02/07/2014, Accepted 18/10/2014, Revised 07/10/2014, Published 25/06/2015

The most important dual relationships of the duality principle include the relationship between node and mesh, and the relationship between branch and branch. They both appear in the patterns of duality, and the latter is also further represented as dual relations of the passive elements, of the active elements, of the controlled-source elements, of the switching elements and also of the two-port coupling elements. This study presents the branch-dualising rule of the duality principle by joining the topological graphs of dual circuits together with physical properties of their elements, proves its adaptability for all the regular circuits and gives a solution for non-regular circuit elements with each just put into a dual element list of the rule one after another after finding its specific dualising mode. The branch-dualising rule is easy and practical for use to obtain the dual circuit diagram directly from its primal, greatly expanding the range of applications of the duality principle.

Inspec keywords: passive networks; graph theory; duality (mathematics); network analysis; active networks

Other keywords: switching elements; two-port coupling elements; branch-dualising rule; passive elements; controlled-source elements; dual circuit diagram; dual relations; active elements; duality principle; regular circuits; topological graphs

Subjects: Combinatorial mathematics; General circuit analysis and synthesis methods

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