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UBC Theses and Dissertations

Synthesis of exponentially-tapered distributed rc networks realizing dirving-point immittance functions Chinn, Henry Ronald

Abstract

In this dissertation, positive-real conformal transformations are used to develop synthesis procedures for the realization of driving-point immittance functions by exponentially- tapered distributed RC networks. These synthesis procedures include the realization by uniform distributed RC networks as a special case. New equivalent circuits are developed for the exponentially- tapered distributed RC network. These differ from the equivalent circuits for the uniform distributed RC network through the presence of positive and negative lumped elements and ideal transformers. It is found that the lumped elements must be eliminated from the equivalent circuits developed for exponentially tapered distributed RC networks before it is possible to apply a positive-real conformal transformation to change the synthesis problem into a lumped LC synthesis problem. Hence, through Richards Theorem, a cascade synthesis procedure for the realization of driving-point immittance functions is developed. Various cascade network realizations are presented. Additional distributed RC sections are used in these realizations to compensate for the lumped elements in the equivalent circuits. Before the synthesis procedure can be applied, it is necessary to approximate any specified driving-point immittance function by a function that is realizable by one of the network configurations presented. A digital computer with plotting facilities is deemed necessary for this purpose.

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