Transient Simulation And Sensitivity Analysis Of Transmission Lines Based On Waveform Relaxation Method

With the continuous decrease of the feature size and the rapid increase of theoperating frequency in modern circuit systems, the problem of transmission lines hasreceived a great deal of attention. A large number of difficulties exist in the simulation anddesign of transmission lines, such as the high-frequency effects, the mixed timedomain/frequency domain difficulty, the substrate nonuniform thermal effects on on-chipinterconnects, the problem of simulating strongly-coupled cables, and the electromagneticinterference problems. The goal of this thesis is to establish a method to deal with suchproblems and difficulties efficiently and accurately.This work mainly focuses on one popular algorithm proposed in recent years–thewaveform relaxation with transverse partitioning method (WR-TP). The WR-TP methodexploits the weak coupling between the transmission lines and is more efficient thanconventional models when dealing with a large number of transmission lines. In addition,parallel implementation is easy to perform for this method. The thesis gives a systematicaldescription of the WR-TP method, extends the application of the method tomulti-parameter cases, and improves the robustness of the method in dealing with stronglycoupled lines. This work also combines the WR-TP method with the finite difference timedomain (FDTD) method, and performs hybrid electromagnetic-circuit analysis.In order to analysis the impact of the nonuniform substrate thermal effect on on-chipinterconnects, the work first presents a recursive implementation of magnitude VectorFitting and Vector Fitting method, establishing a parameterized model for on-chipinterconnects. On the basis of the model, the work then proposes a method extending theapplication of WR-TP to parametric sensitivity analysis. Using the method, the impact ofseveral typical thermal profiles of the substrate on the transient response and thermal sensitivity of on-chip interconnects is investigated.The convergence rate of WR-TP would become significantly low when the methodis used to address strongly coupled transmission lines such as cable bundles. The thesisintroduces a method called joint diagonalization to weaken the coupling among the lines.With the help of joint diagonalizaiton, the WR-TP method can be used to simulate a largenumber of strongly coupled transmission lines efficiently.As for the problem of electromagnetic interference analysis of transmission lines,the thesis points out the importance of the dispersive substrate to the response of thetransmission lines. This work uses an efficient method to deal with multi-pole dispersivedielectrics. The work develops a hybrid method of the finite difference time domain ethod(FDTD) and WR-TP, with which several problems of transmission lines are solvedefficiently and accurately.