A new original method for symbolic analysis of electronic circuits

The main motivation of this dissertation is to contribute to the development of symbolic algebra in scope of electronic circuits analysis. A new original method for symbolic analysis of electronic circuits has been developed and implemented. In contrary to other commonly used methods for symbolic circuit analysis the specificity of this method lies in the fact that it is entirely topology oriented. The proposed procedure provides exact symbolic network function purely by inspecting the topology of the circuit. The method introduces a graph representation of the factorization process, that is constructed directly from a given circuit description. The dissertation is a synthesis of author's published results as well as more recent unpublished material that has emerged during the development of the dissertation. Symbolic analysis is a procedure that generates a circuit function in the form of algebraic expressions such that some or all of the circuit elements and complex frequency are represented by symbolic variables. Unlike the numerical circuit analysis, which provides only quantitative information, symbolic circuit analysis (SCA) provides information of the qualitative contribution of each circuit parameter to the network function. Practically, SCA is mutually complementary to the numerical based electronic circuit analysis. The main drawback of SCA is exponential growth of circuit function intricacy, memory and time requirements with the circuit complexity. Therefore, a hierarchical approach is advisable for treating complex circuits. The technique of hierarchical decomposition of complex circuits results with compact symbolic expressions in nested form. Several methods have been developed to generate nested symbolic expressions of the circuit function using hierarchical decomposition. Some of these methods are graph based and some are matrix based. The most of the modern procedures for symbolic analysis are matrix based. A good representative to the efforts that SCA community spends in this direction is Determinant Decision Diagram method (DDD). Recently presented results proved its efficiency