Efficient representation, stratification, and compression of variational CSM library waveforms using Robust Principle Component Analysis

摘要

In deep sub-micron technology, accurate modeling of output waveforms of library cells under different input slew and load capacitance values is crucial for precise timing and noise analysis of VLSI circuits. Construction of a compact and efficient model of such waveforms becomes even more challenging when manufacturing process and environmental variations are considered. This paper introduces a rigorous and robust foundation to mathematically model output waveforms under sources of variability and to compress the library data. The proposed approach is suitable for today's current source model (CSM) based ASIC libraries. It employs an orthonormal transformation to represent the output waveforms as a linear combination of some appropriately-derived basis waveforms. More significantly Robust Principle Component Analysis (RPCA) is used to stratify the library waveforms into a small number of groups for which different sets of principle components are calculated. This stratification results in a very high compression ratio for the variational CSM library while meeting a maximum error tolerance. Interpolation and further compression is obtained by representing the coefficients as signomial functions of various parameters, e.g., input slew, load capacitance, supply voltage, and temperature. We propose a procedure to calculate the coefficients and power of the signomial functions. Experimental results demonstrate the effectiveness of the proposed variational CSM modeling framework and the stratification-based compression approach.