| The soaring clocking frequency and integration density demand robust and stable power delivery to support tens of millions of transistors switching. To ensure the design quality of power delivery, extensive transient power grid simulations need to be performed to analyze the power delivery fluctuation. However, the traditional circuit simulation engines are not scale well as the complexity of power delivery, as a result, it often takes a long runtime and huge memory requirement to simulate a medium size circuit.; In this thesis, several methods have been proposed to do the power grid simulation and optimization. First, TLM-ADI (transmission-line-modeling alternating-direction-implicit), models the power delivery network as transmission line meshes, and analyzes it by an ADI method. The TLM-ADI is not only with linear runtime and memory requirement but also unconditionally stable. It is then extended to deal with the multi-layer power delivery network.; Then, the basic framework for the hierarchical model order reduction with an emphasis on the signal integrity analysis is established. The proposed algorithm, HMOR (hierarchical model order reduction), performing model reduction for both linear elements and independent sources simultaneously is very suitable for the signal integrity analysis. After that, we extend the concept of HMOR and include the mutual inductances to develop an efficient power delivery analysis method, HiPRIME (hierarchical passivity preserved interconnect macromodeling engine). HiPRIME partitions the power delivery network into several smaller blocks. Then, it establishes a hierarchical power delivery macromodeling methodology which integrates the multiple-port Norton equivalent theorem with model order reduction techniques to generate a compact and accurate model and achieves significant runtime improvement. To further reduce runtime, HiPRIME also develops a multiple level passive model reduction algorithm.; Finally, the problem of minimizing wire area of the power delivery network is considered. A different way is used to derive the adjoint sensitivity analysis without using Tellegen's theorem. This greatly simplifies the discussion of sensitivity analysis. In order to speed up the sensitivity analysis, a model order reduction is utilized to implement the calculation of sensitivity. This efficient analyzer is then combined with nonlinear programming techniques to set up the procedure of optimization. |
