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On the impedance realizing ability of minimal two-element-kind networks

University of British Columbia

The impedance realizing ability of minimal two-element kind networks is considered. As a preamble, a comprehensive survey of relevant mathematics and existing results is presented. An argument based on group theory is used to demonstrate the complex nature of the solution for non-canonic networks. The modal matrix of normal co-ordinate transformation on the cut set admittance matrix is interpreted geometrically as a set of vectors satisfying certain conditions, imposed by the topology and the parameters of the input function of the network, in two Euclidean vector spaces. The existence of the modal matrix, hence the existence of these vectors, is the necessary and sufficient condition for physical realizability. Explicit formulas are developed for third order networks and numerical algorithms for the fourth order networks. A necessary condition is given on the parameters of Z(s) for realizability for networks containing a linear tree of one kind of element.

Text

2011-03-18

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http://hdl.handle.net/2429/32593

Electrical and Computer Engineering

University of British Columbia

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