Application of unilateral and graph techniques to analysis of linear circuits* by H A N A N POTASH and L A W R E N C E P. M c N A M E E University of California Los Angeles, California INTRODUCTION Extensive research is currently under way in developing methods to solve a linear system of first-order differential equations, and in particular the system of equations associated with computer-oriented circuit design. 1-2 The methods presented here are based upon topological and graph theory, which is a natural modeling method for networks since an electrical network is a topological arrangement of electrical components. The information pertinent to circuit analysis and synthesis can be categorized in two phases: first, the topological arrangement of circuit components, and second, the electrical relations within the components. It is advantageous to develop graphical tools to model the circuit in terms of its given topology since this will achieve a convenient linear correspondence between the circuit and its model, in addition to simplifying the modeling procedure. In modeling of the electrical relations inside an element, the application of topological techniques possesses an important advantage over ordinary equations since the topological modeling conserves the cause-and-effect
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