On the congruent transformation of electrical networks for equivalent forms
Parker, Sydney R.
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In this thesis the generation of equivalent networks by means of congruent transformation using a variable transformation matrix applied to the admittance matrix of an n+l node, common datum, network is studied. The ranges of the values of the elements of the transformation matrix which yield passive RLC components for the equivalent network without mutual inductances are considered. When the transformation matrix is diagonal the solution involves a set of linear algebraic inequalities. In the general case, when all the elements of the transformation matrix are present, the solution involves nonlinear algebraic inequalities. The region of passive component realizability consists of a hyper-volume in the space of the elements of the transformation matrix, and the use of exponential searching functions to generate equivalent networks with design constraints is investigated.
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