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# Networks involving ideal transformers

## Citation

Delson, Jerome King (1953) Networks involving ideal transformers. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/JY4D-QP61. https://resolver.caltech.edu/CaltechETD:etd-04222003-140332

## Abstract

The concept of the ideal transformer is presented in terms of flux relations contrasting a non-ideal transformer, which may be represented by an impedance matrix, to an ideal transformer which may not. The interchangeability of the considerations of a transformer, first, as a constraint on the currents (a "multiwinding" transformer) and, second, as a constraint on the voltages (a "multilimb" transformer) is formulated. Mesh and nodal analysis is extended to include networks involving ideal transformers by the use of Lagrange multipliers. These multipliers are eliminated from the equations by a procedure, in terms of compound matrices, that is facilitated by reduction of the transformers to a standard form. The procedure is also interpreted as a set of rules such that the mesh and nodal equations of a general network can be written by inspection. The possible degeneracies in network equations are considered, and a "scattering matrix" procedure presented to cover these cases. The orientation of the branches in a dual network is analyzed and the dual of an ideal transformer is given. The duality concept in electrical networks is considered in terms of matrices that describe the sets of branches belonging to the various meshes (connection matrix) and belonging to the various node-pairs (branch, node-pair matrix). Using the extension of the duality principle to nonplanar networks, a procedure is presented for drawing a network diagram from its connection matrix. As an application, a general procedure is given for finding the electrical analog of a mechanical structure. Also, the role of gyrators and network duality is mentioned. The problem of minimizing the number of transformers in a network is approached by a circuit reduction technique. Networks uniformly dependent on frequency are first synthesized by Cause's technique. The conditions are derived for then eliminating the transformers from this circuit, one by one, for the particular case of a network with three grounded terminal-pairs.

Item Type: Thesis (Dissertation (Ph.D.)) Electrical Engineering, Physics and Mathematics California Institute of Technology Engineering and Applied Science Electrical EngineeringPhysicsMathematics Public (worldwide access) Unknown, Unknown Unknown, Unknown 1 January 1953 CaltechETD:etd-04222003-140332 https://resolver.caltech.edu/CaltechETD:etd-04222003-140332 10.7907/JY4D-QP61 No commercial reproduction, distribution, display or performance rights in this work are provided. 1448 CaltechTHESIS Imported from ETD-db 22 Apr 2003 21 Dec 2019 02:49

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