Techniques for stochastic simulation of complex electromagnetic and circuit systems with uncertainties

This thesis presents a set of tools and methodologies that perform fast stochastic characterization and simulation of uncertainties in electromagnetic and circuit systems. Background information on polynomial chaos and fast stochastic numerical techniques is reviewed, and discussion is offered on comparison of different approaches to stochastic simulations. The formulation for Stochastic LIM, a Stochastic Galerkin Method-based time-domain circuit solver, is presented, and some simulation results are shown comparing the new solver to Monte Carlo techniques using a commercial circuit solver. The simulator is then used to simulate several transmission line problems, including single- and multi-conductor, crosstalk, and coupled-line on a printed circuit board substrate with fiber-weave effect. Stochastic Collocation technique is discussed as a method to characterize multi-level electromagnetic-circuit simulations. A method to use Monte Carlo integration to evaluate interpolation residual is presented. The effectiveness of the proposed method is demonstrated with a high-order problem of electromagnetic waves causing interference on a printed circuit board inside a vehicle with apertures. The effectiveness of the multi-level analysis methodology is demonstrated using eye diagram opening as cost function. Additionally, a wavelet-based Stochastic Collocation technique is introduced to solve circuit problems with resonant behavior. Finally, we discuss the overall work presented in this thesis and discuss several future research directions to extend the results presented here.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Electrical & Computer Engr

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2018

Author dc:creator

• Chen, Xu

Contributors dc:contributor

• Cangellaris, Andreas C.
• Schutt-Ainé, José E.
• Başar, Tamer
• Ravaioli, Umberto

• stochastic, modeling, simulation, latency insertion method, circuit simulation, packaging, uncertainty quantification, stochastic galerkin method, stochastic collocation, monte carlo

Statement dc:rights

• Copyright 2018 Xu Chen

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/101666

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/101666