Fast transient analysis of system-level Power Delivery Networks

This thesis aims to develop a MATLAB code capable of performing a fast transient analysis of a microprocessor's power delivery network (PDN). The initial phase of the research involved implementing the Waveform Relaxation (WR) method, also known as the perturbation approach, to simulate power integrity. The WR method showed promising results when applied to simpler PDNs, successfully validating signal behavior under transient conditions. However, in more complex PDN configurations, the method revealed significant convergence issues, tending towards numerical instability and divergence. To overcome these limitations, the research shifted to the Picard iteration method. This approach, similar to WR, calculates solutions iteratively, improving convergence by summing the computed error at each iteration step until reaching a predetermined accuracy. The Picard iteration method was systematically tested on increasingly complex PDNs, starting with synthetic microprocessor models containing two cores and scaling up to full microprocessor models comprising up to 60 cores. The analysis demonstrated that the Picard iteration method could maintain convergence and reliably assess power integrity, validating signal transmission even in multi-port, multicore architectures. Despite the successful implementation, the work identified numerical challenges arising from the matrix representation of the PDNs. Some of these matrices were found to be poorly conditioned, a factor that complicated achieving MATLAB's machine-level precision. Several measures were taken to mitigate numerical instabilities through algorithmic adjustments and preconditioning techniques, resulting in an acceptable level of accuracy, although still distant from MATLAB's machine precision, yet acceptable from an engineering perspective. Nonetheless, the results confirmed that the approach is robust enough for practical analysis and provides valuable understanding of the power integrity of microprocessors.