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This dissertation, Nonlinear Circuits Modeling and Analysis by the Associated Transform of Volterra Transfer Functions by Yang, Zhang, 張陽, was obtained from The University of Hong Kong (Pokfulam, Hong Kong) and is being sold pursuant to Creative Commons: Attribution 3.0 Hong Kong License. The content of this dissertation has not been altered in any way. We have altered the formatting in order to facilitate the ease of printing and reading of the dissertation. All rights not granted by the above license are retained by the author. Abstract: Model order reduction (MOR) is one of the general techniques in the fields of computeraided design (CAD) and electronic design automation (EDA) which accelerates the flow of electronic simulations and verifications. By MOR, the original circuit, which is described by a set of ordinary differential equations (ODEs), can be trimmed into a much smaller reduced-order model (ROM) in terms of the number of state variables, with approximately the same input-output (I/O) characteristics. Hence, simulations using this ROM will be much more efficient and effective than using the original system.In this thesis, a novel and fast approach of computing the projection matrices serving high-order Volterra transfer functions in the context of weakly and strongly nonlinear MOR is proposed. The innovation is to carry out an association of multivariate Laplace-domain variables in high-order multiple-input multiple-output (MIMO) transfer functions to generate univariate single-s transfer functions. In contrast to conventional projection-based nonlinear MOR which finds projection subspaces about every si in multivariate transfer functions, only that about a single s is required in the proposed approach. This translates into much more compact nonlinear ROMs without compromising accuracy. Different algorithms and their extensions are devised in this thesis. Extensive numerical examples are given to prove and verify the algorithms. DOI: 10.5353/th_b5194797 Subjects: Electronic circuits - Mathematical models

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