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Comparison of standard deviation of the far-end crosstalk voltage obtained from proposed LM approach and MC approach with 20000 samples.
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Distributed networks with embedded parametric uncertainty can be characterized in the frequency-domain by tabulated augmented multiport S or Y-parameter responses based on a stochastic Galerkins formulation of the network equations. In this work, the Loewner Matrix approach is utilized to generate a compact SPICE-compatible macromodel of the stocha...
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Citations
This paper presents a polynomial chaos (PC) formulation based on the concept of dimension reduction for the efficient uncertainty analysis of microwave and RF networks. This formulation exploits a high-dimensional model representation for quantifying the relative effect of each random dimension on the network responses surface. This information acts as problem-dependent sensitivity indices guiding the intelligent identification and subsequent pruning of the statistically unimportant random dimensions from the original parametric space. Performing a PC expansion in the resultant low-dimensional random subspace leads to the recovery of a sparser set of coefficients than that obtained from the full-dimensional random space with negligible loss in accuracy. Novel methodologies to reuse the preliminary PC bases and SPICE simulations required to estimate the sensitivity indices are presented, thereby making the proposed approach more efficient and accurate than standard sparse PC approaches. The validity of the proposed approach is demonstrated using three distributed network examples.
In this paper, a nonintrusive polynomial chaos (PC) approach for the fast multidimensional uncertainty quantification of microwave/RF networks is presented. The key feature of this paper is the development of a linear regression methodology based on sparse D-optimal design of experiments to accurately evaluate the PC coefficients of the network responses. A greedy search algorithm to identify the sparse set of D-optimal design of experiments from within a multidimensional random space has been presented. Additional numerical approaches to further accelerate the search algorithm for high-dimensional random spaces have also been developed.
This paper presents a novel linear regression-based polynomial chaos (PC) approach for the efficient multidimensional uncertainty quantification of general distributed and lumped high-speed circuit networks. The key feature of this paper is the development of a modified Fedorov search algorithm based on the D-optimal criterion that expeditiously locates a highly sparse set of nodes within the multidimensional random space where the original network needs to be probed. Specifically, the number of selected nodes is kept equal to the number of unknown PC coefficients of the network response, thereby making this approach substantially more efficient than the conventional linear regression approach which is based on an oversampling methodology. Additionally, due to the D-optimal criterion, this approach ensures highly accurate recovery of the PC coefficients. The validity of this paper is established through multiple numerical examples.
This paper presents a novel SPICE-compatible stochastic collocation approach for the variability analysis of complex and irregular-shaped power distribution networks (PDNs). The proposed methodology relies on the Stroud cubature rules for locating the sparse set of collocation nodes within the multidimensional random space where the deterministic SPICE simulation of the PDN needs to be performed. The key advantage of the proposed Stroud cubature approach is that the number of collocation nodes required scales linearly with the number of random dimensions as opposed to the exponential or polynomial scaling exhibited by the conventional nonintrusive polynomial chaos approaches, thereby resulting in significantly faster simulations. The validity of the proposed approach for both single-layered and multilayered PDNs characterized by holes/apertures, narrow slots, and irregular geometries is established through multiple numerical examples.
