Electronic Thesis and Dissertation Repository


Master of Engineering Science


Electrical and Computer Engineering


Dr. Anestis Dounavis


In the first part of the thesis, an efficient macromodeling technique based on Loewner Matrix (LM) approach has been presented to model multi-port distributed systems using tabulated noisy data. In the proposed method, Loewner Model data from previous rational approximation are used to create less noisy eigenvectors in an iterative manner. As a result, the biasing effect of the LM model approximated by the noisy data is reduced. It is illustrated that this method improves the accuracy of the Loewner Matrix modeling for noisy frequency data.

In the second part, a fast and robust algorithm is introduced for time-domain simulation of interconnects with few nonlinear elements based on Large Change Sensitivity approach. After macromodeling interconnects, linear parts of the system construct very large matrix. Large linear matrix with nonlinear components makes time domain simulation a Central Processing Unit (CPU) intensive task where inversion (one Lower/Upper (LU) decomposition and one forward/backward substitution) of this large matrix is done at each step of the Newton-Raphson iteration. Using the proposed method, large system matrix is partitioned into linear and nonlinear parts and LU decomposition of linear matrix is done only once in the entire simulation. Nonlinear elements construct a very small matrix compared to large linear matrix. In this proposed method, small matrix is inverted at each Newton iteration. Cost of inverting a small matrix is much cheaper than inverting a very large matrix. Therefore, this approach is faster than the conventional matrix inversion method. Numerical examples are presented illustrating validity and efficiency of the above method.