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Realization of minimal two-element-kind one-port networks Mason, Lloyd Judson

Abstract

A new method of realizing two-element-kind driving-point Impedances is given and illustrated by examples. In this method, networks of any desired topology and having a minimum of elements are utilized. A transformation to normal coordinates forms the basis of the method and, in order to determine network element values, evaluation of the associated transformation matrix is necessary. This matrix is found by formulating and solving a set of multivariable polynomial equations of second degree. The solution to this set of polynomial equations is obtained by a numerical perturbation procedure. To initiate the procedure, a set of element values is chosen, and the network of specified topology is analysed. The corresponding transformation matrix and driving-point impedance are determined from this analysis. The impedance parameters are then perturbed by small amounts in the direction of the specified ones, and the resulting changes in the transformation matrix are calculated. The process is continued until the transformation matrix corresponding to the specified impedance is obtained. A detailed description of the computer program written to carry out the above procedure is Included. A large number of examples of various complexities, including some canonic structures, have been realized by the method. Examples show the superiority of the numerical method to conventional procedures for solving multivariable nonlinear equations. In particular, the choice of the initial set of element values is not required to be close to the final set to achieve convergence to a solution. Some restrictions on the realizability of irreducible complementary tree structures are reported. It is shown that the specification parameters may have local extrema at a point where the Jacobian of the system of polynomial equations vanishes. Examples which support these results are given.

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